indefinite integral: integral 1/squarroot x (1-cos squarerootx) dx

[krys]

integral 1/squarroot x (1-cos squarerootx) dx

u= square root of x / but a question how do I know whats is my u in this type of problem?

du=?

so what I got is -cotsquarex+cscsquarex + C

 

[stapel]

integral 1/squarroot x (1-cos squarerootx) dx

Your formatting is unclear. I think you may mean one of the following:

. . . . .\(\displaystyle \mbox{a) }\,\int\, \left(\dfrac{1}{\sqrt{x\,}}\right)\, \left(1\, -\,\cos\left(\sqrt{x}\right)\right)\, dx\)

. . . . .\(\displaystyle \mbox{b) }\,\int\, \dfrac{1}{\sqrt{x\,}\, \left(1\, -\,\cos\left(\sqrt{x}\right)\right)}\, dx\)

u= square root of x / but a question how do I know whats is my u in this type of problem?

There is no rule, that I'm aware of. You just have to try stuff and see what works. Many times, you'll have to try two or three things to find one that works for you.

du=?

The expression for "du" will be the derivative of the expression for "u".

so what I got is -cotsquarex+cscsquarex + C

I'm sorry, but (1) I don't know what this means (the formatting is unclear) and (2) I don't know for which part you "got" this.

Please reply with clarification, including a clear listing of all of your work and reasoning. Thank you!

 

[krys]

integral ((1)/(squarroot x)(1-cos squareroot x)) dx


integral ((-cot squareroot x)+cscsquareroot of x +C))

I got this because the integral is ((-cot u) +/-(csc u + C))

u=squareroot of x

but can u show me how to get the dirivative of du and why (squareroot x) is u?

 

[pka]

integral 1/squarroot x (1-cos squarerootx) dx

u= square root of x / but a question how do I know whats is my u in this type of problem?

Please read the following and take the advice to heart,

Your formatting is unclear. I think you may mean:
. . . . .\(\displaystyle \mbox{a) }\,\int\, \left(\dfrac{1}{\sqrt{x\,}}\right)\, \left(1\, -\,\cos\left(\sqrt{x}\right)\right)\, dx\)

What is the derivative of \(\displaystyle 2\sqrt{x}-2\sin(\sqrt{x})\).

I wish that u-substitution did not exist.

 

[krys]

I meant B.
I had fixed it

 

[stapel]

I meant B.
I had fixed it

I'm sorry, but I'm not seeing any indication of the post you're saying you edited...?

integral ((1)/(squarroot x)(1-cos squareroot x)) dx

integral ((-cot squareroot x)+cscsquareroot of x +C))

Is the second line a different exercise?

I got this because the integral is ((-cot u) +/-(csc u + C))

What did you "get"? From what? How?

u=squareroot of x

Are you saying that your second integral is some sort of restatement of the first integral? If so, how did you arrive at this?

but can u show me how to get the dirivative of du and why (squareroot x) is u?

I will guess that the first "u" in the above is meant to be "you". As for finding the "derivative" of du, this is not necessary; you need only find du, which is the derivative of the variable expression u.

When you reply, it would really help to keep in mind that we aren't in your classroom, we can't see what you're looking at, and we can't read your mind. Complete sentences, using standard punctuation, spelling, and grammar, are very helpful in conveying meaning. Also, showing all your steps and stating your reasoning clearly (rather than with unreferenced pronouns) can be crucial. Thank you!