What is the integral from 1 to 8 of x^2sqrt(x^3+1) ?

The integral from 1 to 8 of x^2sqrt(x^3+1) is (3078sqrt(57)-4sqrt(2))/9

Popular >

integral from 1 to 8 of x^2sqrt(x^3+1)

\int_{1}^{8} x^{2} x^{3} + 1 d x

\frac{3078 57 - 4 2}{9}

Decimal

2581.41483 \dots

Solution steps

\int_{1}^{8} x^{2} x^{3} + 1 d x

Apply u-substitution

: \int_{2}^{513} \frac{u}{3} d u

= \int_{2}^{513} \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{2}^{513} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{513}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{513}

Compute the boundaries:

102657 - \frac{4 2}{3}

= \frac{1}{3} (102657 - \frac{4 2}{3})

Simplify

= \frac{3078 57 - 4 2}{9}

\int_{1}^{3} (z - 2)^{3} d z

\int_{1}^{x + c} 1 d x

\int_{- 3}^{3} 3 - ∣ x ∣ d x

\int_{0}^{4} 8 - 2 x d x

\int_{0}^{1} (1 - y) y^{n} d y

What is the integral from 1 to 8 of x^2sqrt(x^3+1) ?
The integral from 1 to 8 of x^2sqrt(x^3+1) is (3078sqrt(57)-4sqrt(2))/9