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

The integral of 5x^2e^{2x^3} is 5/6 e^{2x^3}+C

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

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

\frac{5}{6} e^{2 x^{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 5 \cdot \int \frac{e ^{u}}{6} d u

Take the constant out:

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

= 5 \cdot \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= 5 \cdot \frac{1}{6} e^{u}

Substitute back

u = 2 x^{3}

= 5 \cdot \frac{1}{6} e^{2 x^{3}}

Simplify

5 \cdot \frac{1}{6} e^{2 x^{3}} : \frac{5}{6} e^{2 x^{3}}

= \frac{5}{6} e^{2 x^{3}}

Add a constant to the solution

= \frac{5}{6} e^{2 x^{3}} + C

What is the integral of 5x^2e^{2x^3} ?
The integral of 5x^2e^{2x^3} is 5/6 e^{2x^3}+C