What is the integral of cos(x)+2x^{1/2} ?

The integral of cos(x)+2x^{1/2} is sin(x)+4/3 x^{3/2}+C

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integral of cos(x)+2x^{1/2}

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

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

Solution steps

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

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

\int 2 x^{\frac{1}{2}} d x = \frac{4}{3} x^{\frac{3}{2}}

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

Add a constant to the solution

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

What is the integral of cos(x)+2x^{1/2} ?
The integral of cos(x)+2x^{1/2} is sin(x)+4/3 x^{3/2}+C