What is the integral of x^2e^{5x^3} ?

The integral of x^2e^{5x^3} is 1/15 e^{5x^3}+C

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integral of x^2e^{5x^3}

\int x^{2} e^{5 x^{3}} d x

\frac{1}{15} e^{5 x^{3}} + C

Solution steps

\int x^{2} e^{5 x^{3}} d x

Apply u-substitution

: \int \frac{e ^{u}}{15} d u

= \int \frac{e ^{u}}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{15} e^{u}

Substitute back

u = 5 x^{3}

= \frac{1}{15} e^{5 x^{3}}

Add a constant to the solution

= \frac{1}{15} e^{5 x^{3}} + C

\int \frac{4 x + 1}{x - 1} d x

\int 2 x e^{6 x} d x

\int 1 + \frac{x ^{2}}{4 - x ^{2}} d x

\int \frac{2 x + 1}{( x - 1 ) ( x + 2 ) ( x + 5 )} d x

What is the integral of x^2e^{5x^3} ?
The integral of x^2e^{5x^3} is 1/15 e^{5x^3}+C