What is the integral of e^xsqrt(45+e^x) ?

The integral of e^xsqrt(45+e^x) is 2/3 (45+e^x)^{3/2}+C

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integral of e^xsqrt(45+e^x)

\int e^{x} 45 + e^{x} d x

\frac{2}{3} (45 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 45 + e^{x} d x

Apply u-substitution

: \int u d u

= \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 = 45 + e^{x}

= \frac{2}{3} (45 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (45 + e^{x})^{\frac{3}{2}} + C

x d y = 8 y d x

\int \frac{2 x y ^{5}}{9 + x ^{2} y ^{2} - y ^{4}} d x

x \to 9 - lim (\frac{- 7}{( x + 9 )})

x \to 0 lim (8 sin (x) ln (x))

f (x) = x (x + 1), at x = 1

What is the integral of e^xsqrt(45+e^x) ?
The integral of e^xsqrt(45+e^x) is 2/3 (45+e^x)^{3/2}+C