What is the integral of 5xe^{5x} ?

The integral of 5xe^{5x} is e^{5x}x-1/5 e^{5x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5xe^{5x}

\int 5 x e^{5 x} d x

e^{5 x} x - \frac{1}{5} e^{5 x} + C

Solution steps

\int 5 x e^{5 x} d x

Take the constant out:

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

= 5 \cdot \int x e^{5 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{25} d u

= 5 \cdot \int \frac{e ^{u} u}{25} d u

Take the constant out:

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

= 5 \cdot \frac{1}{25} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 5 \cdot \frac{1}{25} (e^{u} u - \int e^{u} d u)

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

= 5 \cdot \frac{1}{25} (e^{u} u - e^{u})

Substitute back

u = 5 x

= 5 \cdot \frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x})

Simplify

5 \cdot \frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x}) : e^{5 x} x - \frac{1}{5} e^{5 x}

= e^{5 x} x - \frac{1}{5} e^{5 x}

Add a constant to the solution

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

\int \frac{1}{x ^{2} - 14 x + 68} d x

\frac{d y}{d x} + (\frac{y}{x}) = 7 x^{3} y^{2}

\frac{\partial}{\partial x} (25 x^{\frac{3}{4}} y^{\frac{1}{4}})

\int - csc^{2} (x) d x

\frac{d y}{d t} = y

What is the integral of 5xe^{5x} ?
The integral of 5xe^{5x} is e^{5x}x-1/5 e^{5x}+C