What is the integral of x^{-4}+x^{1/3} ?

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

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integral of x^{-4}+x^{1/3}

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

s (t) = 3 t + 1

\frac{\partial}{\partial y} (x^{2} yz - x y z^{3})

\frac{d}{d y} (\frac{y}{x})

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

\int_{0}^{π} (1 + sin (x)) d x

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