AP Calculus

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Find the antiderivatives.
1) çãx (x+1) dx

2) ç(x^3-4)/ (x^2) dx

3) ç(3sinx) dx

4) ç(5secxtanx) dx

5) ç(1/x) dx

6) ç(e^x - 2x) dx

7) ç(3)/((1-x^2)^1/2) dx

I picked the antiderivatives i did not know how to do. Please show me how to do a couple of these.

  • AP Calculus -

    the weird symbols in front are supposed be integral signs but watever. i got number 1 and i have the rest i need someone to check the rest.



    4)5secx + c


    6)e^x - x^2

    7) 3sinx

  • AP Calculus -

    #2, I would change
    (x^3-4)/ (x^2) to x - 4x^-2
    and the integral of that is
    (1/2)x^2 + 4x^-1 + c

    check by differentiating my answer, it is right.

    #3, you had
    -cosx, how could you get the 3sinx from that?
    should have been -3cosx + c

    if y = secx
    isn't y' = secxtanx ??
    take care of the 5, and you are done

    #5, you should recognize some standard functions and their derivatives,
    if y = lnx
    isn't y' = 1/x ??? , so .....

    #6, good

    #7, how can the derivative of 3sinx, your answer, possibly be (3)/((1-x^2)^1/2) ?????

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