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Popular >

integral of e^xarcsin(e^x)

Solution

\int e^{x} arcsin (e^{x}) d x

Solution

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

Solution steps

\int e^{x} arcsin (e^{x}) d x

Apply Integration By Parts

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

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

Simplify

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

Add a constant to the solution

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

Popular Examples

integral of 4/(5x^3)

\int \frac{4}{5 x ^{3}} d x

integral of x^4+x^3

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

integral of e^{tan(15x)}sec^2(15x)

\int e^{t a n (15 x)} sec^{2} (15 x) d x

integral of (36)/(1+16x^2)

\int \frac{36}{1 + 16 x ^{2}} d x

integral of (3x^2)/(b^{5x^3)}

\int \frac{3 x ^{2}}{b ^{5 x^{3}}} d x

Frequently Asked Questions (FAQ)

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