Solution assignment 03 Integration by substitution

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Assignment 3

Solve:

$\displaystyle\int{\displaystyle\frac{1}{4}e^{2x+1}}dx$

Solution

First we rewrite this integral:

$\displaystyle\frac{1}{4}\displaystyle\int{e^{2x+1}}dx$

The primitive of:

$e^{2x+1}$

is:

$e^{2x+1}\cdot\displaystyle\frac{1}{2}$

and thus the original integral becomes:

$\displaystyle\frac{1}{4}\displaystyle\int{e^{2x+1}}dx=\displaystyle\frac{1}{4}e^{2x+1}\cdot\displaystyle\frac{1}{2}+C=\displaystyle\frac{1}{8}e^{2x+1}+C$

This result can be verified by differentiation. The chain rule has to be applied.

Return to Assignments Integration by substitution

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Solution assignment 03 Integration by substitution

Assignment 3

Solution

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