What is the integral of ((10)/(x^6)-2e^x+3) ?

The integral of ((10)/(x^6)-2e^x+3) is -2/(x^5)-2e^x+3x+C

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integral of ((10)/(x^6)-2e^x+3)

\int (\frac{10}{x ^{6}} - 2 e^{x} + 3) d x

- \frac{2}{x ^{5}} - 2 e^{x} + 3 x + C

Solution steps

\int \frac{10}{x ^{6}} - 2 e^{x} + 3 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 \frac{10}{x ^{6}} d x - \int 2 e^{x} d x + \int 3 d x

\int \frac{10}{x ^{6}} d x = - \frac{2}{x ^{5}}

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

\int 3 d x = 3 x

= - \frac{2}{x ^{5}} - 2 e^{x} + 3 x

Add a constant to the solution

= - \frac{2}{x ^{5}} - 2 e^{x} + 3 x + C

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\int (2^{- x} + 9 x^{2} e^{x^{3}}) d x

What is the integral of ((10)/(x^6)-2e^x+3) ?
The integral of ((10)/(x^6)-2e^x+3) is -2/(x^5)-2e^x+3x+C