Solution assignment 09 Integration by substitution

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Assignment 9

Solve:

$\displaystyle\int{\displaystyle\frac{1}{(6x+4)^2}}dx$

Solution

We use the following transform:

$u=6x+4$

thus:

$\displaystyle\frac{du}{dx}=6$

thus:

$dx=\displaystyle\frac{1}{6}du$

When we substitute these results in the original integral:

$\displaystyle\int{\displaystyle\frac{1}{(6x+4)^2}}dx=\displaystyle\frac{1}{6}\displaystyle\int{u^{-2}}du=-\displaystyle\frac{1}{6}u^{-1}+C=-\displaystyle\frac{1}{6(6x+4)}+C$

We can verify this result by differentiation. The chain rule has to be applied.

Return to Assignments Integration by substitution

Assignments

Solution assignment 09 Integration by substitution

Assignment 9

Solution

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