What is the integral of 6x^2e^{x^3+2} ?

The integral of 6x^2e^{x^3+2} is 2e^{2+x^3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6x^2e^{x^3+2}

\int 6 x^{2} e^{x^{3} + 2} d x

2 e^{2 + x^{3}} + C

Solution steps

\int 6 x^{2} e^{x^{3} + 2} d x

Take the constant out:

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

= 6 \cdot \int x^{2} e^{x^{3} + 2} d x

Apply Integration By Parts

: \frac{1}{3} e^{x^{3} + 2} x^{3} - \int e^{x^{3} + 2} x^{5} d x

= 6 (\frac{1}{3} e^{x^{3} + 2} x^{3} - \int e^{x^{3} + 2} x^{5} d x)

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

= 6 (\frac{1}{3} e^{x^{3} + 2} x^{3} - \frac{e ^{2}}{3} (e^{x^{3}} x^{3} - e^{x^{3}}))

Simplify

6 (\frac{1}{3} e^{x^{3} + 2} x^{3} - \frac{e ^{2}}{3} (e^{x^{3}} x^{3} - e^{x^{3}})) : 2 e^{2 + x^{3}}

= 2 e^{2 + x^{3}}

Add a constant to the solution

= 2 e^{2 + x^{3}} + C

\int 5 x^{4} sin (x^{5} + 1) d x

\int (\frac{3 x ^{5} - 6 x ^{4} + 5 x ^{3}}{x ^{4}}) d x

\int 3 x e^{4 x^{2}} d x

\int \frac{x ^{2} + 11 x}{( x + 1 ) ^{2} ( x - 1 )} d x

\int \frac{5}{x + 5} d x

What is the integral of 6x^2e^{x^3+2} ?
The integral of 6x^2e^{x^3+2} is 2e^{2+x^3}+C