This is incorrect.

Let

So our integral becomes:

Now continue....

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.

Let

Now, when ,

when ,

So our integral becomes:

Now continue

3.) This one stumped me entirely.

Find the following indefinite integral

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

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

Let

So our integral becomes:

Now continue...

We need the second fundamental theorem of calculus here, i'm not that good with it.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)= _________.

Apply the second fundamental theorem of calculus:

Now just find .......i did pretty much the whole problem, i leave this last bit to you

I guess you could check this manually, it won't be too much work in this case to actually find the integral, evaluate between the limits and then differentiate again. good luck

if you get stuck with any again, say so

EDIT: I verified the last one myself, it checks out