What is the integral of e^{7x+5}x ?

The integral of e^{7x+5}x is 1/7 e^{7x+5}x-1/49 e^{7x+5}+C

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integral of e^{7x+5}x

\int e^{7 x + 5} x d x

\frac{1}{7} e^{7 x + 5} x - \frac{1}{49} e^{7 x + 5} + C

Solution steps

\int e^{7 x + 5} x d x

Apply Integration By Parts

: \frac{1}{7} e^{7 x + 5} x - \int \frac{1}{7} e^{7 x + 5} d x

= \frac{1}{7} e^{7 x + 5} x - \int \frac{1}{7} e^{7 x + 5} d x

\int \frac{1}{7} e^{7 x + 5} d x = \frac{1}{49} e^{7 x + 5}

= \frac{1}{7} e^{7 x + 5} x - \frac{1}{49} e^{7 x + 5}

Add a constant to the solution

= \frac{1}{7} e^{7 x + 5} x - \frac{1}{49} e^{7 x + 5} + C

\int \frac{x ^{6}}{( 8 + x ^{7} ) ^{2}} d x

f (x) = 3 x^{4} + 2 x + 8

sin (1 + x + x^{3})

x^{3} y + y^{3} x - 30

x d y = (x + y) d x

What is the integral of e^{7x+5}x ?
The integral of e^{7x+5}x is 1/7 e^{7x+5}x-1/49 e^{7x+5}+C