What is the integral of 3sqrt(x)+6cos(x) ?

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

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integral of 3sqrt(x)+6cos(x)

\int 3 x + 6 cos (x) d x

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

Solution steps

\int 3 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 3 x d x + \int 6 cos (x) d x

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

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

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

Add a constant to the solution

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

\int \frac{3 + x}{x ^{2} + 2 x + 1} d x

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\int e^{- 0.6 t} d t

\int \frac{e ^{7 x}}{e ^{7 x} + 6} d x

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