What is the integral of 2/3 x^{3/2}-2sin(x) ?

The integral of 2/3 x^{3/2}-2sin(x) is 4/15 x^{5/2}+2cos(x)+C

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integral of 2/3 x^{3/2}-2sin(x)

\int \frac{2}{3} x^{\frac{3}{2}} - 2 sin (x) d x

\frac{4}{15} x^{\frac{5}{2}} + 2 cos (x) + C

Solution steps

\int \frac{2}{3} x^{\frac{3}{2}} - 2 sin (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 \frac{2}{3} x^{\frac{3}{2}} d x - \int 2 sin (x) d x

\int \frac{2}{3} x^{\frac{3}{2}} d x = \frac{4}{15} x^{\frac{5}{2}}

\int 2 sin (x) d x = - 2 cos (x)

= \frac{4}{15} x^{\frac{5}{2}} - (- 2 cos (x))

Simplify

= \frac{4}{15} x^{\frac{5}{2}} + 2 cos (x)

Add a constant to the solution

= \frac{4}{15} x^{\frac{5}{2}} + 2 cos (x) + C

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What is the integral of 2/3 x^{3/2}-2sin(x) ?
The integral of 2/3 x^{3/2}-2sin(x) is 4/15 x^{5/2}+2cos(x)+C