What is the integral of 8x^3+4x-7 ?

The integral of 8x^3+4x-7 is 2x^4+2x^2-7x+C

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integral of 8x^3+4x-7

\int 8 x^{3} + 4 x - 7 d x

2 x^{4} + 2 x^{2} - 7 x + C

Solution steps

\int 8 x^{3} + 4 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 8 x^{3} d x + \int 4 x d x - \int 7 d x

\int 8 x^{3} d x = 2 x^{4}

\int 4 x d x = 2 x^{2}

\int 7 d x = 7 x

= 2 x^{4} + 2 x^{2} - 7 x

Add a constant to the solution

= 2 x^{4} + 2 x^{2} - 7 x + C

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