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

The integral of (x+3)7^{(x+3)^2} is 1/(2ln(7))*7^{(x+3)^2}+C

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

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

\frac{1}{2 ln ( 7 )} \cdot 7^{(x + 3)^{2}} + C

Solution steps

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

Apply u-substitution

: \int 7^{u^{2}} u d u

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

Apply u-substitution

: \int \frac{1}{2 ln ( 7 )} d v

= \int \frac{1}{2 ln ( 7 )} d v

Integral of a constant:

\int a d x = a x

= \frac{1}{2 ln ( 7 )} v

Substitute back

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

Add a constant to the solution

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

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What is the integral of (x+3)7^{(x+3)^2} ?
The integral of (x+3)7^{(x+3)^2} is 1/(2ln(7))*7^{(x+3)^2}+C