What is the integral of (sqrt(t)+cos(t)) ?

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

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integral of (sqrt(t)+cos(t))

\int (t + cos (t)) d t

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

Solution steps

\int t + cos (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t d t + \int cos (t) d t

\int t d t = \frac{2}{3} t^{\frac{3}{2}}

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

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

Add a constant to the solution

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

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