What is the integral of 30t^5e^{-t^6} ?

The integral of 30t^5e^{-t^6} is -5e^{-t^6}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 30t^5e^{-t^6}

\int 30 t^{5} e^{- t^{6}} d t

- 5 e^{- t^{6}} + C

Solution steps

\int 30 t^{5} e^{- t^{6}} d t

Take the constant out:

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

= 30 \cdot \int t^{5} e^{- t^{6}} d t

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= 30 \cdot \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= 30 (- \frac{1}{6} \cdot \int e^{u} d u)

Use the common integral:

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

= 30 (- \frac{1}{6} e^{u})

Substitute back

u = - t^{6}

= 30 (- \frac{1}{6} e^{- t^{6}})

Simplify

30 (- \frac{1}{6} e^{- t^{6}}) : - 5 e^{- t^{6}}

= - 5 e^{- t^{6}}

Add a constant to the solution

= - 5 e^{- t^{6}} + C

\frac{d}{d x} (\frac{x}{9 + x})

\int \frac{x ^{2} + 3 x + 1}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{( e ^{2 x} )}{4 + e ^{4 x}} d x

\int l d l

x \to 1 lim (\frac{9}{x ^{3} - 1})

What is the integral of 30t^5e^{-t^6} ?
The integral of 30t^5e^{-t^6} is -5e^{-t^6}+C