What is the integral from-2 to 1 of 1/((11+5x)^3) ?

The integral from-2 to 1 of 1/((11+5x)^3) is 51/512

Popular >

integral from-2 to 1 of 1/((11+5x)^3)

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{3}} d x

\frac{51}{512}

Decimal

0.099609375

Solution steps

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{3}} d x

Apply u-substitution

: \int_{1}^{16} \frac{1}{5 u ^{3}} d u

= \int_{1}^{16} \frac{1}{5 u ^{3}} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{1}^{16} \frac{1}{u ^{3}} d u

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{1}^{16}

= \frac{1}{5} [- \frac{1}{2 u ^{2}}]_{1}^{16}

Compute the boundaries:

\frac{255}{512}

= \frac{1}{5} \cdot \frac{255}{512}

Simplify

= \frac{51}{512}

\int_{0}^{\frac{π}{2}} sin (x) cos (x) d x

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

\int_{1}^{3} (x + 1)^{4} - (x + 1)^{3} d x

\int_{0}^{6} \frac{1}{4 - x} d x

\int_{- 3}^{3} x d x

What is the integral from-2 to 1 of 1/((11+5x)^3) ?
The integral from-2 to 1 of 1/((11+5x)^3) is 51/512