What is the integral of 2cos(x)-5sqrt(x^3) ?

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

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integral of 2cos(x)-5sqrt(x^3)

\int 2 cos (x) - 5 x^{3} d x

2 sin (x) - 2 x^{\frac{5}{2}} + C

Solution steps

\int 2 cos (x) - 5 x^{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 2 cos (x) d x - \int 5 x^{3} d x

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

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

= 2 sin (x) - 2 x^{\frac{5}{2}}

Add a constant to the solution

= 2 sin (x) - 2 x^{\frac{5}{2}} + C

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