What is the integral of x^3+x^{-4}+x^{3/4} ?

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

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integral of x^3+x^{-4}+x^{3/4}

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

\frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}} + C

Solution steps

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

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

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

\int x^{\frac{3}{4}} d x = \frac{4}{7} x^{\frac{7}{4}}

= \frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{1}{3 x ^{3}} + \frac{4}{7} x^{\frac{7}{4}} + C

e^{10 x}

y^{^{'}} - 7 y = e^{x}

x \to 4 lim (\frac{- 2}{x ^{2} - 16})

\frac{\partial}{\partial x} (x e^{4 y} sin (4 z))

x \to 0 + lim (x - \frac{1}{x})

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