What is the integral of 3x^3e^{2x} ?

The integral of 3x^3e^{2x} is 3(1/2 e^{2x}x^3-3/2 (1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x})))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3x^3e^{2x}

\int 3 x^{3} e^{2 x} d x

3 (\frac{1}{2} e^{2 x} x^{3} - \frac{3}{2} (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}))) + C

Solution steps

\int 3 x^{3} e^{2 x} d x

Take the constant out:

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

= 3 \cdot \int x^{3} e^{2 x} d x

Apply Integration By Parts

: \frac{1}{2} e^{2 x} x^{3} - \int \frac{3}{2} e^{2 x} x^{2} d x

= 3 (\frac{1}{2} e^{2 x} x^{3} - \int \frac{3}{2} e^{2 x} x^{2} d x)

\int \frac{3}{2} e^{2 x} x^{2} d x = \frac{3}{2} (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}))

= 3 (\frac{1}{2} e^{2 x} x^{3} - \frac{3}{2} (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})))

Add a constant to the solution

= 3 (\frac{1}{2} e^{2 x} x^{3} - \frac{3}{2} (\frac{1}{2} e^{2 x} x^{2} - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}))) + C

\frac{\partial}{\partial x} (arctan (x - 2 y))

\int x - x d x

\frac{2}{x}

y^{^{''}} - a y = 0

\int_{1}^{2} x e^{- x^{2}} d x

What is the integral of 3x^3e^{2x} ?
The integral of 3x^3e^{2x} is 3(1/2 e^{2x}x^3-3/2 (1/2 e^{2x}x^2-1/4 (e^{2x}*2x-e^{2x})))+C