What is the integral from 0 to 2 of x^2(x^3+1)^{3/2} ?

The integral from 0 to 2 of x^2(x^3+1)^{3/2} is 484/15

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integral from 0 to 2 of x^2(x^3+1)^{3/2}

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

\frac{484}{15}

Decimal Notation

32.26666 \dots

Solution steps

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

Apply u-substitution

: \int_{1}^{9} \frac{u ^{\frac{3}{2}}}{3} d u

= \int_{1}^{9} \frac{u ^{\frac{3}{2}}}{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_{1}^{9} u^{\frac{3}{2}} d u

Apply the Power Rule

: [\frac{2}{5} u^{\frac{5}{2}}]_{1}^{9}

= \frac{1}{3} [\frac{2}{5} u^{\frac{5}{2}}]_{1}^{9}

Compute the boundaries:

\frac{484}{5}

= \frac{1}{3} \cdot \frac{484}{5}

Simplify

= \frac{484}{15}

3 x^{2}, x^{2} + 4, - 2, 2

ln (\frac{x}{x ^{2} + 6})

\int \frac{- 1}{x} d x

y (x + 7) + y^{^{'}} = 0

\frac{d}{d x} (tan (5 x + 2))

What is the integral from 0 to 2 of x^2(x^3+1)^{3/2} ?
The integral from 0 to 2 of x^2(x^3+1)^{3/2} is 484/15