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# Integration Question! watch

1. I'm stuck on a couple of what i think should be quite simple integration questions so i would really appreciate some help!

First one is: integrate (2x-1) / sqrt x

and the second: integrate cosec^2 (3x+4)

any help at all would be greatly appreciated, cheers
2. first one: (2x-1)/sqrt x =

(2x-1)x^-1/2=

2x^1/2 -x^-1/2

integrate from here.
3. ............
4. 2x-1/sqrt x = (2x-1)(x ^-1/2)
=(x^2 - x)(2x^1/2)+C

i think

5. Which is basic C2 integration.

I'm still looking at the 2nd
6. For the second one, I think you have to solve the cosec^2=1/sin2x and then intergrate that and then use the product rule to solve the whole thing. Or maybe the direct substitution or intergrating by substitution. I might come back and tell you once I've solved it. But I have to go out for a bit might reurn to you in abit//
7. I've done it use the substitution.
integral cosec^2(4+3 x) dx
substitute u = 3 x+4 and du = 3
dx: = 1/3 integral cosec^2(u) du
The integral of cosec^2(u) is -cot(u):
= -(cot(u))/3+c
Substitute back for u = 3 x+4:
= -1/3 cot(3 x+4)+c

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