What is the integral of e^xsqrt(3-e^x) ?

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

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integral of e^xsqrt(3-e^x)

\int e^{x} 3 - e^{x} d x

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

Solution steps

\int e^{x} 3 - 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 = 3 - e^{x}

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

Add a constant to the solution

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

\int 3 (x - 1) y^{3} e^{y (1 - x)} d x

\int + e^{- 0.1 x} d x

x \to 1 lim (ln (x^{\frac{1}{2}}))

\frac{1}{s ^{3} + 5 s}

\frac{1}{1 + s a}

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