What is the integral of (3-x)7^{(3-x)^2} ?

The integral of (3-x)7^{(3-x)^2} is -(7^{(3-x)^2})/(2ln(7))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3-x)7^{(3-x)^2}

\int (3 - x) 7^{(3 - x)^{2}} d x

- \frac{7 ^{(3 - x)^{2}}}{2 ln ( 7 )} + C

Solution steps

\int (3 - x) \cdot 7^{(3 - x)^{2}} d x

Apply u-substitution

= \int - \frac{7 ^{u}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int 7^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{1}{2} \cdot \frac{7 ^{u}}{ln ( 7 )}

Substitute back

u = (3 - x)^{2}

= - \frac{1}{2} \cdot \frac{7 ^{(3 - x)^{2}}}{ln ( 7 )}

Simplify

- \frac{1}{2} \cdot \frac{7 ^{(3 - x)^{2}}}{ln ( 7 )} : - \frac{7 ^{(3 - x)^{2}}}{2 ln ( 7 )}

= - \frac{7 ^{(3 - x)^{2}}}{2 ln ( 7 )}

Add a constant to the solution

= - \frac{7 ^{(3 - x)^{2}}}{2 ln ( 7 )} + C

What is the integral of (3-x)7^{(3-x)^2} ?
The integral of (3-x)7^{(3-x)^2} is -(7^{(3-x)^2})/(2ln(7))+C