What is the integral of 5e^xsqrt(1+e^x) ?

The integral of 5e^xsqrt(1+e^x) is 10/3 (1+e^x)^{3/2}+C

Popular >

integral of 5e^xsqrt(1+e^x)

\int 5 e^{x} 1 + e^{x} d x

\frac{10}{3} (1 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int 5 e^{x} 1 + e^{x} d x

Take the constant out:

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

= 5 \cdot \int e^{x} 1 + e^{x} d x

Apply u-substitution

: \int u d u

= 5 \cdot \int u d u

Apply the Power Rule

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

= 5 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 + e^{x}

= 5 \cdot \frac{2}{3} (1 + e^{x})^{\frac{3}{2}}

Simplify

5 \cdot \frac{2}{3} (1 + e^{x})^{\frac{3}{2}} : \frac{10}{3} (1 + e^{x})^{\frac{3}{2}}

= \frac{10}{3} (1 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{10}{3} (1 + e^{x})^{\frac{3}{2}} + C

x \to - 9 lim (\frac{x ^{2} - 3}{9 - x})

\int_{0}^{\frac{π}{2}} 12 cos^{5} (x) d x

\int \frac{x ^{3}}{3 x ^{2} + 2} d x

\frac{s}{s ( s + 1 )}

\int \frac{e ^{\frac{8}{x}}}{x ^{2}} d x

What is the integral of 5e^xsqrt(1+e^x) ?
The integral of 5e^xsqrt(1+e^x) is 10/3 (1+e^x)^{3/2}+C