What is the integral of 2sqrt(x)+4cos(x) ?

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

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integral of 2sqrt(x)+4cos(x)

\int 2 x + 4 cos (x) d x

\frac{4}{3} x^{\frac{3}{2}} + 4 sin (x) + C

Solution steps

\int 2 x + 4 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 2 x d x + \int 4 cos (x) d x

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

\int 4 cos (x) d x = 4 sin (x)

= \frac{4}{3} x^{\frac{3}{2}} + 4 sin (x)

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} + 4 sin (x) + C

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