What is the integral of (x+1)e^{9x^2+18x} ?

The integral of (x+1)e^{9x^2+18x} is 1/18 e^{9x^2+18x}+C

Popular >

integral of (x+1)e^{9x^2+18x}

\int (x + 1) e^{9 x^{2} + 18 x} d x

\frac{1}{18} e^{9 x^{2} + 18 x} + C

Solution steps

\int (x + 1) e^{9 x^{2} + 18 x} d x

Apply u-substitution

: \int \frac{e ^{u}}{18} d u

= \int \frac{e ^{u}}{18} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{18} e^{u}

Substitute back

u = 9 x^{2} + 18 x

= \frac{1}{18} e^{9 x^{2} + 18 x}

Add a constant to the solution

= \frac{1}{18} e^{9 x^{2} + 18 x} + C

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 8 sin (3 x), y (0) = 1, y^{^{'}} (0) = 2

x \to 1 lim ((9 x^{2}) + 30 x + 25)

4 y

\int x^{25} sin (x^{26}) d x

e^{5}

What is the integral of (x+1)e^{9x^2+18x} ?
The integral of (x+1)e^{9x^2+18x} is 1/18 e^{9x^2+18x}+C