What is the integral of (10x+2)e^{5x^2+2x+8} ?

The integral of (10x+2)e^{5x^2+2x+8} is e^{5x^2+2x+8}+C

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integral of (10x+2)e^{5x^2+2x+8}

\int (10 x + 2) e^{5 x^{2} + 2 x + 8} d x

e^{5 x^{2} + 2 x + 8} + C

Solution steps

\int (10 x + 2) e^{5 x^{2} + 2 x + 8} 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 = 5 x^{2} + 2 x + 8

= e^{5 x^{2} + 2 x + 8}

Add a constant to the solution

= e^{5 x^{2} + 2 x + 8} + C

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What is the integral of (10x+2)e^{5x^2+2x+8} ?
The integral of (10x+2)e^{5x^2+2x+8} is e^{5x^2+2x+8}+C