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 $$\int_{-1}^0 e^{\sqrt{x}}dx+ \int_{-1}^0 dx$$.