What is the integral of-(58)/((3t+2)^2) ?

The integral of-(58)/((3t+2)^2) is (58)/(3(3t+2))+C

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integral of-(58)/((3t+2)^2)

\int - \frac{58}{( 3 t + 2 ) ^{2}} d t

\frac{58}{3 ( 3 t + 2 )} + C

Solution steps

\int - \frac{58}{( 3 t + 2 ) ^{2}} d t

Take the constant out:

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

= - 58 \cdot \int \frac{1}{( 3 t + 2 ) ^{2}} d t

Apply u-substitution

: \int \frac{1}{3 u ^{2}} d u

= - 58 \cdot \int \frac{1}{3 u ^{2}} d u

Take the constant out:

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

= - 58 \cdot \frac{1}{3} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - 58 \cdot \frac{1}{3} (- \frac{1}{u})

Substitute back

u = 3 t + 2

= - 58 \cdot \frac{1}{3} (- \frac{1}{3 t + 2})

Simplify

- 58 \cdot \frac{1}{3} (- \frac{1}{3 t + 2}) : \frac{58}{3 ( 3 t + 2 )}

= \frac{58}{3 ( 3 t + 2 )}

Add a constant to the solution

= \frac{58}{3 ( 3 t + 2 )} + C

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What is the integral of-(58)/((3t+2)^2) ?
The integral of-(58)/((3t+2)^2) is (58)/(3(3t+2))+C