What is the integral of 7te^{6t} ?

The integral of 7te^{6t} is 7/36 (6e^{6t}t-e^{6t})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7te^{6t}

\int 7 t e^{6 t} d t

\frac{7}{36} (6 e^{6 t} t - e^{6 t}) + C

Solution steps

\int 7 t e^{6 t} d t

Take the constant out:

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

= 7 \cdot \int t e^{6 t} d t

Apply u-substitution

: \int \frac{e ^{u} u}{36} d u

= 7 \cdot \int \frac{e ^{u} u}{36} d u

Take the constant out:

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

= 7 \cdot \frac{1}{36} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 7 \cdot \frac{1}{36} (e^{u} u - \int e^{u} d u)

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

= 7 \cdot \frac{1}{36} (e^{u} u - e^{u})

Substitute back

u = 6 t

= 7 \cdot \frac{1}{36} (e^{6 t} \cdot 6 t - e^{6 t})

Simplify

7 \cdot \frac{1}{36} (e^{6 t} \cdot 6 t - e^{6 t}) : \frac{7}{36} (6 e^{6 t} t - e^{6 t})

= \frac{7}{36} (6 e^{6 t} t - e^{6 t})

Add a constant to the solution

= \frac{7}{36} (6 e^{6 t} t - e^{6 t}) + C

\int \frac{- 3}{x} d x

\int 2 π cos (π) x d x

\int \frac{1}{1 + sec ( a x )} d x

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

\int - sin (x) cos^{3} (x) d x

What is the integral of 7te^{6t} ?
The integral of 7te^{6t} is 7/36 (6e^{6t}t-e^{6t})+C