What is the integral of xe^{12x} ?

The integral of xe^{12x} is 1/144 (e^{12x}*12x-e^{12x})+C

Popular >

integral of xe^{12x}

\int x e^{12 x} d x

\frac{1}{144} (e^{12 x} \cdot 12 x - e^{12 x}) + C

Solution steps

\int x e^{12 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{144} d u

= \int \frac{e ^{u} u}{144} d u

Take the constant out:

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

= \frac{1}{144} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{1}{144} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{144} (e^{u} u - e^{u})

Substitute back

u = 12 x

= \frac{1}{144} (e^{12 x} \cdot 12 x - e^{12 x})

Add a constant to the solution

= \frac{1}{144} (e^{12 x} \cdot 12 x - e^{12 x}) + C

\frac{\partial}{\partial x} (- 4 x)

\int \frac{1}{2 x - 5} d x

\frac{\partial}{\partial x} (2 zy)

x = \frac{( y - 4 ) ^{2}}{4}, y = 7 - x

\frac{d}{d x} (- 243 sin (3 x))

What is the integral of xe^{12x} ?
The integral of xe^{12x} is 1/144 (e^{12x}*12x-e^{12x})+C