What is the integral of 2sqrt(x)+6cos(x) ?

The integral of 2sqrt(x)+6cos(x) is 4/3 x^{3/2}+6sin(x)+C

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integral of 2sqrt(x)+6cos(x)

\int 2 x + 6 cos (x) d x

\frac{4}{3} x^{\frac{3}{2}} + 6 sin (x) + C

Solution steps

\int 2 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 2 x d x + \int 6 cos (x) d x

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

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

= \frac{4}{3} x^{\frac{3}{2}} + 6 sin (x)

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} + 6 sin (x) + C

\int (25 - x^{2})^{\frac{1}{2}} d x

\frac{d}{d x} (\frac{1}{e ^{x} - 1})

e^{3 x} (- 2 sin (2 x) + 3 cos (2 x))

\int x^{5} + 2 x^{3} + x d x

\frac{d}{d x} (x + 60)

What is the integral of 2sqrt(x)+6cos(x) ?
The integral of 2sqrt(x)+6cos(x) is 4/3 x^{3/2}+6sin(x)+C