What is the integral of e^xsqrt(2-e^x) ?

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

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integral of e^xsqrt(2-e^x)

\int e^{x} 2 - e^{x} d x

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

Solution steps

\int e^{x} 2 - 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 = 2 - e^{x}

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (x^{2} y z^{3})

f (x) = 1 - 4 x

\frac{d}{d x} (\frac{4}{( 1 + 2 x ) ^{2}})

\frac{d}{d x} (ln (17 x))

x \to - 5 lim (3 x - ∣ x + 5 ∣)

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