What is the integral of (t^3)/(e^{2t^4)} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (t^3)/(e^{2t^4)}

\int \frac{t ^{3}}{e ^{2 t^{4}}} d t

- \frac{1}{8 e ^{2 t^{4}}} + C

Solution steps

\int \frac{t ^{3}}{e ^{2 t^{4}}} d t

Apply u-substitution

: \int \frac{1}{8 e ^{u}} d u

= \int \frac{1}{8 e ^{u}} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{1}{e ^{u}} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \frac{1}{8} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= \frac{1}{8} (- \frac{1}{v})

Substitute back

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

Simplify

\frac{1}{8} (- \frac{1}{e ^{2 t^{4}}}) : - \frac{1}{8 e ^{2 t^{4}}}

= - \frac{1}{8 e ^{2 t^{4}}}

Add a constant to the solution

= - \frac{1}{8 e ^{2 t^{4}}} + C

\int 4 x sinh (2 x) d x

\int \frac{1}{sin ( x ) + cos ( x ) + 3} d x

\int \frac{t + 1}{t ^{2} + 2 t + 3} d t

\int (x^{2} - 6 x + 4)^{14} (x - 3) d x

\int \frac{1}{w ^{\frac{1}{3}}} d w

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