What is the integral of e^xsqrt(5-e^x) ?

The integral of e^xsqrt(5-e^x) is -2/3 (5-e^x)^{3/2}+C

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integral of e^xsqrt(5-e^x)

\int e^{x} 5 - e^{x} d x

- \frac{2}{3} (5 - e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 5 - 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 = 5 - e^{x}

= - \frac{2}{3} (5 - e^{x})^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (5 - e^{x})^{\frac{3}{2}} + C

\frac{x ^{2} - 3 x - 4}{x - 2}

\int 2 cos^{2} (x) sin (x) d x

\int e^{- 4 x} \cdot x d x

- \frac{3 x ^{2}}{4 y ^{2}}

2 x^{2} + 15

What is the integral of e^xsqrt(5-e^x) ?
The integral of e^xsqrt(5-e^x) is -2/3 (5-e^x)^{3/2}+C