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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int 5 sin^{3} (2 x co) s^{3} 2 x d x

y^{^{''}} + 4 y = 4 sin (2 t)

y = \frac{x}{( 1 + x ^{2} )}

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

\frac{\partial}{\partial y} (\frac{cos ( y )}{x z ^{2}})

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