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

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

Popular >

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

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

\frac{4 2}{9}

Decimal Notation

0.62853 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{2} \frac{u}{3} d u

= \int_{0}^{2} \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_{0}^{2} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2}

Compute the boundaries:

\frac{4 2}{3}

= \frac{1}{3} \cdot \frac{4 2}{3}

Simplify

= \frac{4 2}{9}

\int \frac{x ^{2} + 3 x}{x + 4} d x

\int (\frac{e ^{4 x} - 5}{e ^{2 x}}) d x

y^{^{'}} - \frac{5}{x} y = \frac{y ^{5}}{x ^{3}}, y (1) = 1

f (x) = (x^{2} - 5)^{2}

\int_{- 2}^{- 1} (15 x^{- 4}) d x

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