What is the integral of (5x-7)e^{5x-7} ?

The integral of (5x-7)e^{5x-7} is e^{5x-7}x-8/5 e^{5x-7}+C

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integral of (5x-7)e^{5x-7}

\int (5 x - 7) e^{5 x - 7} d x

e^{5 x - 7} x - \frac{8}{5} e^{5 x - 7} + C

Solution steps

\int (5 x - 7) e^{5 x - 7} d x

Expand

(5 x - 7) e^{5 x - 7} : 5 e^{5 x - 7} x - 7 e^{5 x - 7}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add similar elements:

- \frac{1}{5} e^{5 x - 7} - \frac{7}{5} e^{5 x - 7} = - \frac{8}{5} e^{5 x - 7}

= e^{5 x - 7} x - \frac{8}{5} e^{5 x - 7}

Add a constant to the solution

= e^{5 x - 7} x - \frac{8}{5} e^{5 x - 7} + C

\int t e^{- 3 t} d t

g (t) = \frac{t - t}{t ^{\frac{1}{9}}}

x^{2} y^{^{''}} + 7 x y^{^{'}} + 5 y = 0

\frac{d}{d x} (\frac{2 + 3 x}{x ^{2}})

\int sin^{18} (x) cos^{3} (x) d x

What is the integral of (5x-7)e^{5x-7} ?
The integral of (5x-7)e^{5x-7} is e^{5x-7}x-8/5 e^{5x-7}+C