What is the integral of (7x^2+x^{-4}) ?

The integral of (7x^2+x^{-4}) is (7x^3)/3-1/(3x^3)+C

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integral of (7x^2+x^{-4})

\int (7 x^{2} + x^{- 4}) d x

\frac{7 x ^{3}}{3} - \frac{1}{3 x ^{3}} + C

Solution steps

\int 7 x^{2} + x^{- 4} 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 7 x^{2} d x + \int x^{- 4} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int x^{- 4} d x = - \frac{1}{3 x ^{3}}

= \frac{7 x ^{3}}{3} - \frac{1}{3 x ^{3}}

Add a constant to the solution

= \frac{7 x ^{3}}{3} - \frac{1}{3 x ^{3}} + C

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What is the integral of (7x^2+x^{-4}) ?
The integral of (7x^2+x^{-4}) is (7x^3)/3-1/(3x^3)+C