What is the integral of (3x^2+2x)e^{x^3+x^2} ?

The integral of (3x^2+2x)e^{x^3+x^2} is e^{x^3+x^2}+C

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integral of (3x^2+2x)e^{x^3+x^2}

\int (3 x^{2} + 2 x) e^{x^{3} + x^{2}} d x

e^{x^{3} + x^{2}} + C

Solution steps

\int (3 x^{2} + 2 x) e^{x^{3} + x^{2}} d x

Apply u-substitution

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = x^{3} + x^{2}

= e^{x^{3} + x^{2}}

Add a constant to the solution

= e^{x^{3} + x^{2}} + C

What is the integral of (3x^2+2x)e^{x^3+x^2} ?
The integral of (3x^2+2x)e^{x^3+x^2} is e^{x^3+x^2}+C