# Integration Problem

Hey everyone,
I can't seem to figure out how to do this integral. If anyone could help that would be great. I would appreciate some hints/advice, rather than just the answer. Thanks!
The question is:
Evaluate the indefinite integral:
(4sin(x)+3tan(x))dx
Ok... So i know you can take the integral of each term seperatly because it is a sum and that is a principle of integrals.... so i get the first part to be -4cos(x). However I am not sure how to evalue the antiderivative of 3tan(x). If anyone could help that would be great!
Thanks again.

StatusX
Homework Helper
Noting that tan x = sin x/cos x, you can integrate by subsitution using u=cos x.

ok...... so i tried that.
so with the substitution you end up with du/u whose antiderivative is -ln(absolute value)U. U is cosx so it is -ln(abs)cosx. Moving the negative sign into the logarithm gives ln(abs)secx. So my final answer would be...
4cosx+3ln(abs)secx. Im not to sure this is right though. Could one of you smart math people check and if i made an error somewhere point me in the right direction.
Thanks alot for the help!

TD
Homework Helper
Watch your signs, the antiderivative of sin(x) is -cos(x).

Oh yes...
-4cosx+3ln(abs)secx???
Thanks for pointing that out. (i think i fixed it)

Another quick question that I cant seem to figure out...
Find the definite integral from 0 to 1 of:
x^2((5x+6)^(1/2))
I thought this may be another substitution question but I cant see what to substitute. Any help would be great!

Last edited:
TD
Homework Helper
I was referring to the term 4cos(x) which should actually be -4cos(x)

Tx
For the second, let u= 5x + 6 from there it is easy to see that x^2 = (u-6)^2/25, then expand and integrate.

I dont really understand that Tx. If i let U=5xt6 i end up with x^2(U)^(1/2)(du/5) which doesnt seem to help me in any way. Some more advice would be good! I appreciate the help!