What is the integral of \sqrt[3]{x}+cos(3x) ?

The integral of \sqrt[3]{x}+cos(3x) is 3/4 x^{4/3}+1/3 sin(3x)+C

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integral of \sqrt[3]{x}+cos(3x)

\frac{3}{4} x^{\frac{4}{3}} + \frac{1}{3} sin (3 x) + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= \frac{3}{4} x^{\frac{4}{3}} + \frac{1}{3} sin (3 x)

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} + \frac{1}{3} sin (3 x) + C

\frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2})

\int \frac{cos ( x )}{( 1 + sin ( x ) ) ^{5}} d x

\frac{d}{d x} ((e^{x^{2}} + 4)^{2} \cdot (4 x)^{3 x})

\frac{16}{s ( s ^{2} + 16 )}

x \to 0 lim (\frac{2}{sin ( 3 x )})

What is the integral of \sqrt[3]{x}+cos(3x) ?
The integral of \sqrt[3]{x}+cos(3x) is 3/4 x^{4/3}+1/3 sin(3x)+C