Solution assignment 01 Integration by substitution

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Assignment 1

Solve:

\displaystyle\int{(5x+2)^{10}}dx

Solution

The primitive is:

\displaystyle\frac{1}{11}(5x+2)^{11}.\displaystyle\frac{1}{5}

and thus the result is:

\displaystyle\int{(5x+2)^{10}}dx=\displaystyle\frac{1}{55}(5x+2)^{11}+C

This is a correct result as can be verified by differentiation. The chain rule has to be applied.

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