What is the integral of (143)/((x+7)^2) ?

The integral of (143)/((x+7)^2) is -(143)/(x+7)+C

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integral of (143)/((x+7)^2)

\int \frac{143}{( x + 7 ) ^{2}} d x

- \frac{143}{x + 7} + C

Solution steps

\int \frac{143}{( x + 7 ) ^{2}} d x

Take the constant out:

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

= 143 \cdot \int \frac{1}{( x + 7 ) ^{2}} d x

Apply u-substitution

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

= 143 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 143 (- \frac{1}{u})

Substitute back

u = x + 7

= 143 (- \frac{1}{x + 7})

Simplify

143 (- \frac{1}{x + 7}) : - \frac{143}{x + 7}

= - \frac{143}{x + 7}

Add a constant to the solution

= - \frac{143}{x + 7} + C

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What is the integral of (143)/((x+7)^2) ?
The integral of (143)/((x+7)^2) is -(143)/(x+7)+C