What is the integral of-x^7e^{x^8-7}-2x ?

The integral of-x^7e^{x^8-7}-2x is -1/8 e^{x^8-7}-x^2+C

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integral of-x^7e^{x^8-7}-2x

\int - x^{7} e^{x^{8} - 7} - 2 x d x

- \frac{1}{8} e^{x^{8} - 7} - x^{2} + C

Solution steps

\int - x^{7} e^{x^{8} - 7} - 2 x 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 x^{7} e^{x^{8} - 7} d x - \int 2 x d x

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

\int 2 x d x = x^{2}

= - \frac{1}{8} e^{x^{8} - 7} - x^{2}

Add a constant to the solution

= - \frac{1}{8} e^{x^{8} - 7} - x^{2} + C

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What is the integral of-x^7e^{x^8-7}-2x ?
The integral of-x^7e^{x^8-7}-2x is -1/8 e^{x^8-7}-x^2+C