What is the integral of (8x^{3/5}-3x^{-4}+4) ?

The integral of (8x^{3/5}-3x^{-4}+4) is 5x^{8/5}+1/(x^3)+4x+C

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integral of (8x^{3/5}-3x^{-4}+4)

\int (8 x^{\frac{3}{5}} - 3 x^{- 4} + 4) d x

5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C

Solution steps

\int 8 x^{\frac{3}{5}} - 3 x^{- 4} + 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 8 x^{\frac{3}{5}} d x - \int 3 x^{- 4} d x + \int 4 d x

\int 8 x^{\frac{3}{5}} d x = 5 x^{\frac{8}{5}}

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

\int 4 d x = 4 x

= 5 x^{\frac{8}{5}} - (- \frac{1}{x ^{3}}) + 4 x

Simplify

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x

Add a constant to the solution

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C

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\int tanh (x) ln (cosh (x)) d x

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What is the integral of (8x^{3/5}-3x^{-4}+4) ?
The integral of (8x^{3/5}-3x^{-4}+4) is 5x^{8/5}+1/(x^3)+4x+C