Integral question again. (indefinite integral)
int (x/(x+1)^1/2)

Question

Integral question again. (indefinite integral) 
int (x/(x+1)^1/2)

kainui · Answer

$$\int\limits_{}^{}\frac{ xdx }{ \sqrt{x+1} }$$ right?

jennychan12 · Answer

$$\int\limits \frac{ x }{ \sqrt{x+1} }dx$$
sorry forgot the dx

jennychan12 · Answer

yeah.

jennychan12 · Answer

wait sorry no.

jennychan12 · Answer

i typed the question wrong. 
$$\int\limits \frac{ x }{ \sqrt{x-1} } dx$$

kainui · Answer

Either way, you can use u-substitution in several clever ways that aren't always immediately obvious. Want me to tell you or would you like to guess first?

jennychan12 · Answer

i tried u sub with u = x - 1 and i got du = dx and i tried plugging in x = u + 1 but it seems to make it even more complicated...

kainui · Answer

Yes, you're on the right track. =D

kainui · Answer

Remember your exponent rules to simplify it into just a regular old polynomial.

jennychan12 · Answer

can u rewrite it as x(x-1)^-1/2 ?

jennychan12 · Answer

ohhhhh i see what ur saying.....

kainui · Answer

Hmm I don't know, I wouldn't take that route lol.

kainui · Answer

Yes, good. I think. =D

jennychan12 · Answer

yeah so u simplify the u stuff to get int(u^1/2 + u^-1/2)dx right?

jennychan12 · Answer

whoops i meant du

kainui · Answer

Wait, I think it's - not +, or maybe I'm backwards, I don't remember what the question was again lol. But yeah, you got it, exactly.

jennychan12 · Answer

i typed the question slightly wrong. the botom should be rad(x-1)

kainui · Answer

Yeah it is +, when I solved it I had already done it the way you posted it first, so you're right. Now you an integrate that right?

jennychan12 · Answer

yeah. thanks :)