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

The integral from 1 to 2 of 1/((2x+1)^3) is 4/225

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

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

\frac{4}{225}

Decimal

0.01777 \dots

Solution steps

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

Apply u-substitution

= \int_{3}^{5} \frac{1}{2 u ^{3}} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{3}^{5} \frac{1}{u ^{3}} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{8}{225}

= \frac{1}{2} \cdot \frac{8}{225}

Simplify

= \frac{4}{225}

What is the integral from 1 to 2 of 1/((2x+1)^3) ?
The integral from 1 to 2 of 1/((2x+1)^3) is 4/225