What is the integral of 27xe^{3x} ?

The integral of 27xe^{3x} is 3(3e^{3x}x-e^{3x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 27xe^{3x}

\int 27 x e^{3 x} d x

3 (3 e^{3 x} x - e^{3 x}) + C

Solution steps

\int 27 x e^{3 x} d x

Take the constant out:

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

= 27 \cdot \int x e^{3 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{9} d u

= 27 \cdot \int \frac{e ^{u} u}{9} d u

Take the constant out:

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

= 27 \cdot \frac{1}{9} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 27 \cdot \frac{1}{9} (e^{u} u - \int e^{u} d u)

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

= 27 \cdot \frac{1}{9} (e^{u} u - e^{u})

Substitute back

u = 3 x

= 27 \cdot \frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x})

Simplify

27 \cdot \frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x}) : 3 (3 e^{3 x} x - e^{3 x})

= 3 (3 e^{3 x} x - e^{3 x})

Add a constant to the solution

= 3 (3 e^{3 x} x - e^{3 x}) + C

\int (e^{x} + 4^{x}) d x

\int sin (3 x) cos^{4} (3 x) d x

\int (7 x - 1) e^{2 x} d x

\int 0.04 x + 27 d x

\int x tan^{2} (x^{2}) sec^{2} (x^{2}) d x

What is the integral of 27xe^{3x} ?
The integral of 27xe^{3x} is 3(3e^{3x}x-e^{3x})+C