What is the integral of 1/(2sqrt(x))+sin(x) ?

The integral of 1/(2sqrt(x))+sin(x) is sqrt(x)-cos(x)+C

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integral of 1/(2sqrt(x))+sin(x)

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

x - cos (x) + C

Solution steps

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

\int \frac{1}{2 x} d x = x

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

= x - cos (x)

Add a constant to the solution

= x - cos (x) + C

\frac{d y}{d x} + \frac{2}{x} y = \frac{1}{x ^{4}}

\int - 4 e^{- t} d t

\int \frac{1}{( 3 x - 1 ) ^{2}} d x

\int_{0}^{4} 9 e^{- 2 x} d x

(arcsin (x))^{3}

What is the integral of 1/(2sqrt(x))+sin(x) ?
The integral of 1/(2sqrt(x))+sin(x) is sqrt(x)-cos(x)+C