What is the integral of 8*cos(x)+1/(sqrt(x))+e^{3x} ?

The integral of 8*cos(x)+1/(sqrt(x))+e^{3x} is 8sin(x)+2sqrt(x)+1/3 e^{3x}+C

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integral of 8*cos(x)+1/(sqrt(x))+e^{3x}

\int 8 \cdot cos (x) + \frac{1}{x} + e^{3 x} d x

8 sin (x) + 2 x + \frac{1}{3} e^{3 x} + C

Solution steps

\int 8 cos (x) + \frac{1}{x} + e^{3 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 cos (x) d x + \int \frac{1}{x} d x + \int e^{3 x} d x

\int 8 cos (x) d x = 8 sin (x)

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

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= 8 sin (x) + 2 x + \frac{1}{3} e^{3 x}

Add a constant to the solution

= 8 sin (x) + 2 x + \frac{1}{3} e^{3 x} + C

What is the integral of 8*cos(x)+1/(sqrt(x))+e^{3x} ?
The integral of 8*cos(x)+1/(sqrt(x))+e^{3x} is 8sin(x)+2sqrt(x)+1/3 e^{3x}+C