What is the integral from-1 to 3 of 1/((x+2)^3) ?

The integral from-1 to 3 of 1/((x+2)^3) is 12/25

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integral from-1 to 3 of 1/((x+2)^3)

\int_{- 1}^{3} \frac{1}{( x + 2 ) ^{3}} d x

\frac{12}{25}

Solution steps

\int_{- 1}^{3} \frac{1}{( x + 2 ) ^{3}} d x

Apply u-substitution

: \int_{1}^{5} \frac{1}{u ^{3}} d u

= \int_{1}^{5} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{1}^{5}

= [- \frac{1}{2 u ^{2}}]_{1}^{5}

Compute the boundaries:

\frac{12}{25}

= \frac{12}{25}

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What is the integral from-1 to 3 of 1/((x+2)^3) ?
The integral from-1 to 3 of 1/((x+2)^3) is 12/25