What is the integral of (5sqrt(x)+4sin(x)) ?

The integral of (5sqrt(x)+4sin(x)) is 10/3 x^{3/2}-4cos(x)+C

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integral of (5sqrt(x)+4sin(x))

\int (5 x + 4 sin (x)) d x

\frac{10}{3} x^{\frac{3}{2}} - 4 cos (x) + C

Solution steps

\int 5 x + 4 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 5 x d x + \int 4 sin (x) d x

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

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

= \frac{10}{3} x^{\frac{3}{2}} - 4 cos (x)

Add a constant to the solution

= \frac{10}{3} x^{\frac{3}{2}} - 4 cos (x) + C

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What is the integral of (5sqrt(x)+4sin(x)) ?
The integral of (5sqrt(x)+4sin(x)) is 10/3 x^{3/2}-4cos(x)+C