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

The integral of (2-x)3^{(2-x)^2} is -1/(2ln(3))*3^{(2-x)^2}+C

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

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

- \frac{1}{2 ln ( 3 )} \cdot 3^{(2 - x)^{2}} + C

Solution steps

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

Apply u-substitution

: \int - 3^{u^{2}} u d u

= \int - 3^{u^{2}} u d u

Take the constant out:

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

= - \int 3^{u^{2}} u d u

Apply u-substitution

: \int \frac{1}{2 ln ( 3 )} d v

= - \int \frac{1}{2 ln ( 3 )} d v

Integral of a constant:

\int a d x = a x

= - \frac{1}{2 ln ( 3 )} v

Substitute back

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

Add a constant to the solution

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

\int_{0}^{3} \frac{1}{9 - x ^{2}} d x

\frac{d}{d x} (- A B^{- x} + C)

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

\int \frac{x + 1}{x + 2} d x

\int \frac{x}{x + 20} d x

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