What is the integral from 0 to 1 of 1/((x+1)^5) ?

The integral from 0 to 1 of 1/((x+1)^5) is 15/64

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integral from 0 to 1 of 1/((x+1)^5)

\int_{0}^{1} \frac{1}{( x + 1 ) ^{5}} d x

\frac{15}{64}

Decimal

0.234375

Solution steps

\int_{0}^{1} \frac{1}{( x + 1 ) ^{5}} d x

Apply u-substitution

= \int_{1}^{2} \frac{1}{u ^{5}} d u

Apply the Power Rule

= [- \frac{1}{4 u ^{4}}]_{1}^{2}

Compute the boundaries:

\frac{15}{64}

= \frac{15}{64}

What is the integral from 0 to 1 of 1/((x+1)^5) ?
The integral from 0 to 1 of 1/((x+1)^5) is 15/64