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

The integral of (x^3-3sqrt(x)+x^{-5/4}) is (x^4)/4-2x^{3/2}-4/(\sqrt[4]{x)}+C

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \int x^{3} - 3 x + \frac{1}{x ^{\frac{5}{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 x^{3} d x - \int 3 x d x + \int \frac{1}{x ^{\frac{5}{4}}} d x

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

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

\int \frac{1}{x ^{\frac{5}{4}}} d x = - \frac{4}{x ^{\frac{1}{4}}}

= \frac{x ^{4}}{4} - 2 x^{\frac{3}{2}} - \frac{4}{x ^{\frac{1}{4}}}

Apply radical rule:

Add a constant to the solution

What is the integral of (x^3-3sqrt(x)+x^{-5/4}) ?
The integral of (x^3-3sqrt(x)+x^{-5/4}) is (x^4)/4-2x^{3/2}-4/(\sqrt[4]{x)}+C