What is the integral of e^xarcsin(sqrt(1-e^{2x)}) ?

The integral of e^xarcsin(sqrt(1-e^{2x)}) is e^xarcsin(sqrt(1-e^{2x)})-sqrt(1-e^{2x)}+C

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integral of e^xarcsin(sqrt(1-e^{2x)})

\int e^{x} arcsin (1 - e^{2 x}) d x

e^{x} arcsin (1 - e^{2 x}) - 1 - e^{2 x} + C

Solution steps

\int e^{x} arcsin (1 - e^{2 x}) d x

Apply Integration By Parts

: e^{x} arcsin (1 - e^{2 x}) - \int - \frac{e ^{2 x}}{1 - e ^{2 x}} d x

= e^{x} arcsin (1 - e^{2 x}) - \int - \frac{e ^{2 x}}{1 - e ^{2 x}} d x

\int - \frac{e ^{2 x}}{1 - e ^{2 x}} d x = 1 - e^{2 x}

= e^{x} arcsin (1 - e^{2 x}) - 1 - e^{2 x}

Add a constant to the solution

= e^{x} arcsin (1 - e^{2 x}) - 1 - e^{2 x} + C

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

\int (2 x - 3) (4 x^{2} + 6 x + 9) d x

\int \frac{x ^{3}}{x ^{4} - 4} d x

\int \frac{1}{( 5 - 2 x ) ^{2}} d x

What is the integral of e^xarcsin(sqrt(1-e^{2x)}) ?
The integral of e^xarcsin(sqrt(1-e^{2x)}) is e^xarcsin(sqrt(1-e^{2x)})-sqrt(1-e^{2x)}+C