What is the integral of 6/((x+3)^2) ?

The integral of 6/((x+3)^2) is -6/(x+3)+C

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integral of 6/((x+3)^2)

\int \frac{6}{( x + 3 ) ^{2}} d x

- \frac{6}{x + 3} + C

Solution steps

\int \frac{6}{( x + 3 ) ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int \frac{1}{( x + 3 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= 6 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 6 (- \frac{1}{u})

Substitute back

u = x + 3

= 6 (- \frac{1}{x + 3})

Simplify

6 (- \frac{1}{x + 3}) : - \frac{6}{x + 3}

= - \frac{6}{x + 3}

Add a constant to the solution

= - \frac{6}{x + 3} + C

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