I am working on substitution and I get far with each question but then I get near the end of evaluating the integrals with differentiation (or antiderivatives, can't remember off the top off my head) and I get stuck or get the wrong answer.

here are the ones I am stuck on(I will try multiple forms of writing it):

1.)

Evaluate the indefinite integral:

Integral bar--cos(x)--dx/1 = _______________ + C

-----------4sin(x)+8

(I started by substituting "4sin(x) + 8" with "u".

I got in the end (1/4)(1/(-cos(x)+8)) + C .

2.)

Evaluate the definite integral

Integral bar High# e^6, Low#1 or [1,e^6] if you prefer.----dx-----

------------------------------------------------------x(1+ln(x))

= _______________

I substituted "u" for 1+ln(x) because 1/x can be used to replace the 1/x in the main integral.

I worked this one so much I got lost.

u = 1 + ln(x)

du = 1/x dx or dx/x

= integral bar [1,7] (<= replacing the old values since I changed it.) du 1/u

=-(1+1/x) and a couple other versions as well.

3.) This one stumped me entirely.

Find the following indefinite integral

integral bar----x-----dx

--------------sqrt(x+8)

The last isn't too hard to get the first part but then I tried the second part the same way and I got a wrong answer.

4.) If f(x) = integral bar [x,x^2] (t^2)dt , then

f '(-3)= _________.