What is the integral of (x+1)e^{5x^2+10x} ?

The integral of (x+1)e^{5x^2+10x} is 1/10 e^{5x^2+10x}+C

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integral of (x+1)e^{5x^2+10x}

\int (x + 1) e^{5 x^{2} + 10 x} d x

\frac{1}{10} e^{5 x^{2} + 10 x} + C

Solution steps

\int (x + 1) e^{5 x^{2} + 10 x} d x

Apply u-substitution

: \int \frac{e ^{u}}{10} d u

= \int \frac{e ^{u}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{10} e^{u}

Substitute back

u = 5 x^{2} + 10 x

= \frac{1}{10} e^{5 x^{2} + 10 x}

Add a constant to the solution

= \frac{1}{10} e^{5 x^{2} + 10 x} + C

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\frac{d}{d x} (7 x (sin (x) + cos (x)))

\frac{d x}{d t} = 2 e^{t} - 2

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\int \frac{x}{( x + 1 ) ^{3}} d x

What is the integral of (x+1)e^{5x^2+10x} ?
The integral of (x+1)e^{5x^2+10x} is 1/10 e^{5x^2+10x}+C