What is the integral of e^x-9x^8+sin(x) ?

The integral of e^x-9x^8+sin(x) is e^x-x^9-cos(x)+C

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integral of e^x-9x^8+sin(x)

\int e^{x} - 9 x^{8} + sin (x) d x

e^{x} - x^{9} - cos (x) + C

Solution steps

\int e^{x} - 9 x^{8} + sin (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 e^{x} d x - \int 9 x^{8} d x + \int sin (x) d x

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

\int 9 x^{8} d x = x^{9}

\int sin (x) d x = - cos (x)

= e^{x} - x^{9} - cos (x)

Add a constant to the solution

= e^{x} - x^{9} - cos (x) + C

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What is the integral of e^x-9x^8+sin(x) ?
The integral of e^x-9x^8+sin(x) is e^x-x^9-cos(x)+C