What is the integral of (3x^2+4)e^{x^3+4x} ?

The integral of (3x^2+4)e^{x^3+4x} is e^{x^3+4x}+C

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integral of (3x^2+4)e^{x^3+4x}

\int (3 x^{2} + 4) e^{x^{3} + 4 x} d x

e^{x^{3} + 4 x} + C

Solution steps

\int (3 x^{2} + 4) e^{x^{3} + 4 x} d x

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = x^{3} + 4 x

= e^{x^{3} + 4 x}

Add a constant to the solution

= e^{x^{3} + 4 x} + C

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What is the integral of (3x^2+4)e^{x^3+4x} ?
The integral of (3x^2+4)e^{x^3+4x} is e^{x^3+4x}+C