What is the integral of e^xsqrt(8-e^x) ?

The integral of e^xsqrt(8-e^x) is -2/3 (8-e^x)^{3/2}+C

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integral of e^xsqrt(8-e^x)

\int e^{x} 8 - e^{x} d x

- \frac{2}{3} (8 - e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 8 - 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 = 8 - e^{x}

= - \frac{2}{3} (8 - e^{x})^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (8 - e^{x})^{\frac{3}{2}} + C

\frac{d}{d a} (sin^{4} (a) - cos^{4} (a) + cos^{2} (a))

\frac{d}{d x} (x (x + 1))

\frac{d}{d x} (4 x^{3} - \frac{2}{x ^{3}})

y^{^{''}} - y^{^{'}} = - 12

\int \frac{4}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

What is the integral of e^xsqrt(8-e^x) ?
The integral of e^xsqrt(8-e^x) is -2/3 (8-e^x)^{3/2}+C