What is the integral of 8sqrt(x)+6cos(x) ?

The integral of 8sqrt(x)+6cos(x) is 16/3 x^{3/2}+6sin(x)+C

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integral of 8sqrt(x)+6cos(x)

\int 8 x + 6 cos (x) d x

\frac{16}{3} x^{\frac{3}{2}} + 6 sin (x) + C

Solution steps

\int 8 x + 6 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 8 x d x + \int 6 cos (x) d x

\int 8 x d x = \frac{16}{3} x^{\frac{3}{2}}

\int 6 cos (x) d x = 6 sin (x)

= \frac{16}{3} x^{\frac{3}{2}} + 6 sin (x)

Add a constant to the solution

= \frac{16}{3} x^{\frac{3}{2}} + 6 sin (x) + C

What is the integral of 8sqrt(x)+6cos(x) ?
The integral of 8sqrt(x)+6cos(x) is 16/3 x^{3/2}+6sin(x)+C