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

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

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

\int 3 x - cos (x) d x

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

Solution steps

\int 3 x - cos (x) 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 3 x d x - \int cos (x) d x

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

\int cos (x) d x = sin (x)

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

Add a constant to the solution

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

y = (x^{4} + \frac{2}{x}), (1, 3)

\frac{d ^{2}}{d x ^{2}} (ln (x + 1))

\int (x^{2} + 3) ln (2 x) d x

\int \frac{9}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

y = x^{5 x}

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