What is the integral of e^tsqrt(e^t+3) ?

The integral of e^tsqrt(e^t+3) is 2/3 (e^t+3)^{3/2}+C

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integral of e^tsqrt(e^t+3)

\int e^{t} e^{t} + 3 d t

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

Solution steps

\int e^{t} e^{t} + 3 d t

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 = e^{t} + 3

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

Add a constant to the solution

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

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What is the integral of e^tsqrt(e^t+3) ?
The integral of e^tsqrt(e^t+3) is 2/3 (e^t+3)^{3/2}+C