What is the integral of 5xe^{8x} ?

The integral of 5xe^{8x} is 5/64 (8e^{8x}x-e^{8x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5xe^{8x}

\int 5 x e^{8 x} d x

\frac{5}{64} (8 e^{8 x} x - e^{8 x}) + C

Solution steps

\int 5 x e^{8 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^{8 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{64} d u

= 5 \cdot \int \frac{e ^{u} u}{64} d u

Take the constant out:

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

= 5 \cdot \frac{1}{64} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 5 \cdot \frac{1}{64} (e^{u} u - \int e^{u} d u)

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

= 5 \cdot \frac{1}{64} (e^{u} u - e^{u})

Substitute back

u = 8 x

= 5 \cdot \frac{1}{64} (e^{8 x} \cdot 8 x - e^{8 x})

Simplify

5 \cdot \frac{1}{64} (e^{8 x} \cdot 8 x - e^{8 x}) : \frac{5}{64} (8 e^{8 x} x - e^{8 x})

= \frac{5}{64} (8 e^{8 x} x - e^{8 x})

Add a constant to the solution

= \frac{5}{64} (8 e^{8 x} x - e^{8 x}) + C

\int \frac{e ^{x}}{e ^{x} + 2} d x

\frac{d}{d x} (\frac{5 - 3 x}{x ^{2} + 3 x})

cos (\frac{π x}{2})

\int_{0}^{1} 4 x arccos (x) d x

\int \frac{13 x ^{3}}{2 + x ^{2}} d x

What is the integral of 5xe^{8x} ?
The integral of 5xe^{8x} is 5/64 (8e^{8x}x-e^{8x})+C