Thread: integration problems - urgent

Hi,

Attached document contain question rearding indefinite integrals.

Can someone help to provide solution for all three questions ASAP.

Apologise for improper way of defining the question as i don't have the software in which we can draw maths problem nicely.

Thanks in advance.

Best Regards,
Lalit Chugh[B]

1.

1/cot(x) is simply tan(x), so this integral is really

Use this identity and it should be easy.

2.

Just distribute the square root of x and use basic power rules.

Originally Posted by Jameson

1.

1/cot(x) is simply tan(x), so this integral is really

Use this identity and it should be easy.

_____________

for this problem, i think just rewrite the function in term tanx = sinx/cosx
then, you will flip cosx into the denominator. It will come out like this, intergal of (sinx/cos^2x)dx
next step, using the sub methods

let u = cosx, du = - sinxdx

-du = sinxdx

then just jam that into the integral.

u will get something like du/u^2

bring u^2 on top : u-2

take the integral. u^-1/-1 or

1/-cosx + c will become your answer

Originally Posted by distance

_____________

for this problem, i think just rewrite the function in term tanx = sinx/cosx
then, you will flip cosx into the denominator. It will come out like this, intergal of (sinx/cos^2x)dx
next step, using the sub methods

let u = cosx, du = - sinxdx

-du = sinxdx

then just jam that into the integral.

u will get something like du/u^2

bring u^2 on top : u-2

take the integral. u^-1/-1 or

1/-cosx + c will become your answer

i think the answer is tanx - x + c

i agree with you.

Answer comes to: tanx - x + c

Yes. This is the correct answer. Using the substitution I gave you get . And thus the answer follows.