# Examples of General Power of Integration

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

We have integral

Here $f\left( x \right) = {x^2} + 7x + 3$ implies that $f'\left( x \right) = 2x + 7$
We observe that derivation of given function is in the given problem, so using general power formula of integration, we have

Example: Integrate ${\sin ^6}x\cos x$ with respect to $x$.

Consider the function to be integrate

Here $f\left( x \right) = \sin x$ implies that $f'\left( x \right) = \cos x$
We observe that derivation of given function is in the given problem, so using general power formula of integration, we have