Need Help PLEASE!! (antiderivatives)

[nam2w]

Find the antiderivative of each:

1) 1/(x+7)

2) e^x/(1+e^x): This is e to the x divided by 1 plus e to the x

3) t cos (t^2)

4) x^2 e^x^3: This is x squared times e to the x to the third

5) Find the average value of f(x) = sinx on the interval [0, pi].

PLEASE HELP!

 

[stapel]

1) Hint: For y = ln(x), what is dy/dx?

2) I would suggest u-substitution on the denominator.

3) Try u-substitution on the argument of the cosine.

4) Assuming you mean "x² e^{x^3}", try u-substitution on the power on the exponential.

5) The "average" value is just the total "area under the curve", divided by the length of the interval.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.