can anyone solve these integration problems?

Question

Integrate each of the following functions using substitution, finding the most general antiderivative.

Also enter u, the function of x that you substitute.

If your answer requires a constant of integration, enter it as c.

*S represents the integral

#1
S(4 x^3 + 3 )/sqrt(x^4+3 x+4)dx = ?????
u=???

#2
S(ln x )^5/x dx =???
u=???


#3
Sx^2/(4 x^3 + 2) dx =???
u=??

Answer 1

#1. A quick peek at the denominator indicates this is du/sqrt u. You can do the rest.
#2 rewrite num. as 5 ln x. Then u= ln x,
du= 1/x dx. So we have 5S udu = 5/2 u^2 or
5 ln x +c1.
#3 u = 4x^3+2 and du= 12x^2. Then the integration converts to S (1/12) du/u or
1/12 ln (4x^3+2) + C1.

Answer 2

a million.tan^3?=tan? tan^2?=tan? (sec^2?-a million) separate into 2 integrals and replace tan? in the 1st vital and for the 2d the respond is log|sec?| 2. replace x^2 = t 3.do with the aid of factors.... this is.. keeping x as ur 2d function answer wud be -x csc(x) + ?csc(x)dx = -x csc(x) + log|csc(x)-cot(x)| 4.num = A(diff of denominator) + B x = A(2x-4) + B A=a million/2 B= 2 den separate the integrals as a million/2 ?(2x-4)/(x^2-4x-5) dx + 2?a million/(x^2-4x-5) dx = a million/2 log|x^2-4x-5| + 2H the place H=?a million/(x^2-4x-5) dx = ?a million/[(x-2)^2 - 3^2] dx = a million/6 log|x-5/x-a million|