What is the integral from 0 to x of 1/((x+100)^3) ?

The integral from 0 to x of 1/((x+100)^3) is -1/(2(x+100)^2)+1/20000

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integral from 0 to x of 1/((x+100)^3)

\int_{0}^{x} \frac{1}{( x + 100 ) ^{3}} d x

- \frac{1}{2 ( x + 100 ) ^{2}} + \frac{1}{20000}

Solution steps

\int_{0}^{x} \frac{1}{( x + 100 ) ^{3}} d x

Apply u-substitution

: \int_{100}^{x + 100} \frac{1}{u ^{3}} d u

= \int_{100}^{x + 100} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{100}^{x + 100}

= [- \frac{1}{2 u ^{2}}]_{100}^{x + 100}

Compute the boundaries:

- \frac{1}{2 ( x + 100 ) ^{2}} + \frac{1}{20000}

= - \frac{1}{2 ( x + 100 ) ^{2}} + \frac{1}{20000}

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What is the integral from 0 to x of 1/((x+100)^3) ?
The integral from 0 to x of 1/((x+100)^3) is -1/(2(x+100)^2)+1/20000