What is the integral of x/(sqrt(8+x^2))+3e^{4x} ?

The integral of x/(sqrt(8+x^2))+3e^{4x} is sqrt(8+x^2)+3/4 e^{4x}+C

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integral of x/(sqrt(8+x^2))+3e^{4x}

\int \frac{x}{8 + x ^{2}} + 3 e^{4 x} d x

8 + x^{2} + \frac{3}{4} e^{4 x} + C

Solution steps

\int \frac{x}{8 + x ^{2}} + 3 e^{4 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 \frac{x}{8 + x ^{2}} d x + \int 3 e^{4 x} d x

\int \frac{x}{8 + x ^{2}} d x = 8 + x^{2}

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

= 8 + x^{2} + \frac{3}{4} e^{4 x}

Add a constant to the solution

= 8 + x^{2} + \frac{3}{4} e^{4 x} + C

What is the integral of x/(sqrt(8+x^2))+3e^{4x} ?
The integral of x/(sqrt(8+x^2))+3e^{4x} is sqrt(8+x^2)+3/4 e^{4x}+C