What is the integral of-4x^3e^{4x^2} ?

The integral of-4x^3e^{4x^2} is -1/8 (4e^{4x^2}x^2-e^{4x^2})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-4x^3e^{4x^2}

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

- \frac{1}{8} (4 e^{4 x^{2}} x^{2} - e^{4 x^{2}}) + C

Solution steps

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

Take the constant out:

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

= - 4 \cdot \int x^{3} e^{4 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u} u}{32} d u

= - 4 \cdot \int \frac{e ^{u} u}{32} d u

Take the constant out:

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

= - 4 \cdot \frac{1}{32} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= - 4 \cdot \frac{1}{32} (e^{u} u - \int e^{u} d u)

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

= - 4 \cdot \frac{1}{32} (e^{u} u - e^{u})

Substitute back

u = 4 x^{2}

= - 4 \cdot \frac{1}{32} (e^{4 x^{2}} \cdot 4 x^{2} - e^{4 x^{2}})

Simplify

- 4 \cdot \frac{1}{32} (e^{4 x^{2}} \cdot 4 x^{2} - e^{4 x^{2}}) : - \frac{1}{8} (4 e^{4 x^{2}} x^{2} - e^{4 x^{2}})

= - \frac{1}{8} (4 e^{4 x^{2}} x^{2} - e^{4 x^{2}})

Add a constant to the solution

= - \frac{1}{8} (4 e^{4 x^{2}} x^{2} - e^{4 x^{2}}) + C

y^{^{'}} + y = y^{- 2}

\int e^{3 t} (e^{3 t} - 1) d t

\frac{( s + 1 )}{( s + 1 ) ^{2} + 1}

(- 1, 6), (7, - 2)

\int \frac{1}{10 x + 1} d x

What is the integral of-4x^3e^{4x^2} ?
The integral of-4x^3e^{4x^2} is -1/8 (4e^{4x^2}x^2-e^{4x^2})+C