What is the integral from 0 to 2 of 1/((x+3)^3) ?

The integral from 0 to 2 of 1/((x+3)^3) is 8/225

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integral from 0 to 2 of 1/((x+3)^3)

\int_{0}^{2} \frac{1}{( x + 3 ) ^{3}} d x

\frac{8}{225}

Decimal

0.03555 \dots

Solution steps

\int_{0}^{2} \frac{1}{( x + 3 ) ^{3}} d x

Apply u-substitution

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

Apply the Power Rule

= [- \frac{1}{2 u ^{2}}]_{3}^{5}

Compute the boundaries:

\frac{8}{225}

= \frac{8}{225}

What is the integral from 0 to 2 of 1/((x+3)^3) ?
The integral from 0 to 2 of 1/((x+3)^3) is 8/225