What is the integral of (1/(sqrt(4-9x^2))+e^{4x}) ?

The integral of (1/(sqrt(4-9x^2))+e^{4x}) is 1/3 arcsin(3/2 x)+1/4 e^{4x}+C

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integral of (1/(sqrt(4-9x^2))+e^{4x})

\int (\frac{1}{4 - 9 x ^{2}} + e^{4 x}) d x

\frac{1}{3} arcsin (\frac{3}{2} x) + \frac{1}{4} e^{4 x} + C

Solution steps

\int \frac{1}{4 - 9 x ^{2}} + 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{1}{4 - 9 x ^{2}} d x + \int e^{4 x} d x

\int \frac{1}{4 - 9 x ^{2}} d x = \frac{1}{3} arcsin (\frac{3}{2} x)

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

= \frac{1}{3} arcsin (\frac{3}{2} x) + \frac{1}{4} e^{4 x}

Add a constant to the solution

= \frac{1}{3} arcsin (\frac{3}{2} x) + \frac{1}{4} e^{4 x} + C

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What is the integral of (1/(sqrt(4-9x^2))+e^{4x}) ?
The integral of (1/(sqrt(4-9x^2))+e^{4x}) is 1/3 arcsin(3/2 x)+1/4 e^{4x}+C