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

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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

= \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

y^{^{'}} = \frac{7 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

\frac{d}{d x} (\frac{3}{2} tan (x))

\int \frac{y}{y ^{2} + 9} d y

e^{7}

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