## Maclaurin Series of Sqrt(1+x)

In this tutorial we shall derive the series expansion of $$\sqrt {1 + x} $$ by using Maclaurin’s series expansion… Click here to read more

From basic to higher mathematics

In this tutorial we shall derive the series expansion of $$\sqrt {1 + x} $$ by using Maclaurin’s series expansion… Click here to read more

In this tutorial we shall discuss an example of the slope of a tangent to any curve at some given… Click here to read more

In this tutorial we shall look at the differentials of independent and dependent variables. Some applications of differentials will be… Click here to read more

In this tutorial we shall look at the use of differentials to approximate the value of $$\cos {44^ \circ }$$…. Click here to read more

In this tutorial we shall look at the use differentials to approximate the value of $$\tan {61^ \circ }$$. The… Click here to read more

In this tutorial we shall develop the differentials to approximate the value of $$\sqrt {49.5} $$. The nearest number to… Click here to read more

In this tutorial we shall develop the differentials to approximate the value of $$\csc {61^ \circ }$$. The nearest number… Click here to read more

In this tutorial we shall discuss the application of differentials to approximate any real problem. Let’s look at an example…. Click here to read more

Integral calculus is an important part of calculus, as important as differential calculus. In differential calculus we study the relationship… Click here to read more

The power rule of integration is an important and fundamental formula in integral calculus. We already know that the inverse… Click here to read more

Example: Integrate $$\frac{{{x^2} – 2{x^4}}}{{{x^4}}}$$ with respect to $$x$$. Consider the function to be integrated \[I = \int {\frac{{{x^2} –… Click here to read more

The general power rule of integration is another important formula of integration, and this rule needs th derivative of the… Click here to read more

Example: Evaluate the integral $$\int {\left( {2x + 7} \right){{\left( {{x^2} + 7x + 3} \right)}^{\frac{4}{5}}}dx} $$ with respect to… Click here to read more

The integration of one over $$x$$ is another important formula of integration. The integration of one over $$X$$ is of… Click here to read more

The integration of derivative over function of $$x$$ is another important formula of integration. The integration of derivative over function… Click here to read more

The integration of $$e^x$$ is another important formula of integral calculus. This integral belongs to the exponential formulae and is… Click here to read more

The integration of $$e$$ to the power $$x$$ of a function is a general formula of exponential functions and this… Click here to read more

The integration of any constant of power $$x$$ is important and belongs to the exponential formulae. It is one of… Click here to read more

The integration of any constant power of a function is a general formula of exponential functions, and this formula needs… Click here to read more

Integration of the sine function is an important integral formula in integral calculus. This integral belongs to the trigonometric formulae…. Click here to read more

Integration of the cosine function is an important integral formula in integral calculus. This integral belongs to the trigonometric formulae…. Click here to read more

In this tutorial we will prove the formula of tangent integral which is another important formula in integral calculus. This… Click here to read more

In this tutorial we will prove the formula of cotangent integral which is another important formula in integral calculus. This… Click here to read more

In this tutorial we will prove the formula of secant integral which is another important formula in integral calculus. This… Click here to read more

In this tutorial we will prove the formula of cosecant integral which is another important formula in integral calculus. This… Click here to read more

Integration of the secant tangent function is an important integral formula in integral calculus, and this integral belongs to the… Click here to read more

Integration of the cosecant cotangent function is an important integral formula in integral calculus, and this integral belongs to the… Click here to read more

Integration of secant squared of x is an important integral formula in integral calculus, and this integral belongs to the… Click here to read more

Integration of cosecant squared of x is an important integral formula in integral calculus, and this integral belongs to the… Click here to read more

In this tutorial we shall use different substitutions before evaluating the integrals. Sometimes an integration is very complicated to solve,… Click here to read more

In order to evaluate some particular integrals, some substitutions play very important roles in making the integral easier to evaluate…. Click here to read more

Example: Evaluate the integral \[\int {\frac{{{{\sin }^3}\left( {\ln \ln x} \right)\cos \left( {\ln \ln x} \right)}}{{x\ln x}}} dx\] with respect… Click here to read more

In this tutorial we shall develop a technique that will help us to evaluate a wide variety of integrals that… Click here to read more

In this tutorial we shall explain integration of the natural logarithmic function $$\ln x$$. It is an important integral function,… Click here to read more

In this tutorial we shall explain the integration of the sine inverse function $${\sin ^{ – 1}}x$$. It is an… Click here to read more

In this tutorial we shall explain the integration of the cosine inverse function $${\cos ^{ – 1}}x$$. It is an… Click here to read more

The tangent inverse function $${\tan ^{ – 1}}x$$ it is an important integral function, but it has no direct method… Click here to read more

The integral of cotangent inverse $${\cot ^{ – 1}}x$$ it is an important integral function, but it has no direct… Click here to read more

The integral of secant inverse $${\sec ^{ – 1}}x$$ it is an important integral function, but it has no direct… Click here to read more

The integral of inverse cosecant $${\csc ^{ – 1}}x$$ it is an important integral function, but it has no direct… Click here to read more

In this tutorial we shall find the integral of inverse sine squared function, and it is another important integration. To… Click here to read more

In this tutorial we shall find the integral of the inverse cosine squared function, and it is another important integration…. Click here to read more

In this tutorial we shall find the integral of $${\left( {\ln x} \right)^2}$$ function, and it is another important integration…. Click here to read more

In this tutorial we shall explain another very important type of integral. The integration of sine inverse is of the… Click here to read more

In this tutorial we shall discuss the integral of the secant cubed of $$X$$, and this integration can be evaluated… Click here to read more

In this tutorial we shall discuss the integral of cosecant cubed of $$X$$, and this integration can be evaluated by… Click here to read more

The integration of the hyperbolic sine function is an important integral formula in integral calculus. This integral belongs to the… Click here to read more

The integration of the hyperbolic cosine function is an important integral formula in integral calculus. This integral belongs to the… Click here to read more

In this tutorial we shall discuss the integration of the hyperbolic secant square function, and this integral is an important… Click here to read more