Integration by parts and substitution help

[KAG1188]

Integration by parts and substitution help!

Homework Statement

∫0
-1 e ^√x+1

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

I'm sorry, but I simply cannot figure out what that integral is intended to be.

Is that \int_{-1}^0 e^{\sqrt{x+1}} dx or \int_{-1}^0 e^{\sqrt{x}+ 1} dx or \int_{-1}^0 e^{\sqrt{x}}+ 1 dx?

If it is the first, take u= \sqrt{x+1}= (x+1)^{1/2} so that du= (1/2)(x+1)^{-1/2}dx so that (x+1)^{1/2}du= u du= dx. When x= -1, u= 0, when x= 0, u= 1 The integral becomes
\int_0^1 ue^{u}du
and can be done by "integration by parts".

If the second, write it as e\int_{-1}^0 e^{\sqrt{x}}dx and let u= \sqrt{x}.

If the third, write it as \int_{-1}^0 e^{\sqrt{x}}dx+ \int_{-1}^0 dx.