What is the integral from 0 to 1 of xe^{x^3} ?

The integral from 0 to 1 of xe^{x^3} is

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integral from 0 to 1 of xe^{x^3}

\int_{0}^{1} x e^{x^{3}} d x

Solution steps

\int_{0}^{1} x e^{x^{3}} d x

Apply u-substitution

: \int_{0}^{1} \frac{e ^{u^{\frac{3}{2}}}}{2} d u

= \int_{0}^{1} \frac{e ^{u^{\frac{3}{2}}}}{2} 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_{0}^{1} e^{u^{\frac{3}{2}}} d u

Use the nonelementary integral:

Compute the boundaries:

\int_{- 1}^{8} (- x^{2} + 10 x) d x

\int_{0}^{1} 20 (x^{3} - x^{4}) d x

\int_{0}^{1} (5 x^{4} - 3 x^{2} + 1) d x

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

\int_{0}^{9} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

What is the integral from 0 to 1 of xe^{x^3} ?
The integral from 0 to 1 of xe^{x^3} is