What is the integral of e^xsqrt(1-e^x) ?

The integral of e^xsqrt(1-e^x) is -2/3 (1-e^x)^{3/2}+C

Popular >

integral of e^xsqrt(1-e^x)

\int e^{x} 1 - e^{x} d x

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

Solution steps

\int e^{x} 1 - e^{x} d x

Apply u-substitution

: \int - u d u

= \int - u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= - \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 - e^{x}

= - \frac{2}{3} (1 - e^{x})^{\frac{3}{2}}

Add a constant to the solution

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

e^{x^{2} y} = x + y

\frac{\partial}{\partial x} (\frac{x}{x ^{2} - y ^{2}})

\frac{d}{d x} (- \frac{8}{1 - 8 x})

(2 - x^{2})^{\frac{1}{2}}

\int_{0}^{1} \frac{1}{x + 1} d x

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