In this tutorial we will prove the formula of tangent integral which is also an important formula in integral calculus; this integral belongs to trigonometric formulae.
The integration of tangent function is of the form
To prove this formula, consider
Using the derivative formulas and , we have
Integrating both sides of equation (i) with respect to , we have
As we know that by definition integration is the inverse process of derivative, so the integral sign and on the right side will cancel each other, i.e.
Further we can prove this formula in another form as,
We have given integration of the form
Here we have then
Using the formula of integration,
Other Integral Formulas of Tangent Function:
The other formulas of tangent integral with angle of sine is in the form of function are given as
Example: Evaluate the integral with respect to
We have integral
Using the formula , we have