Question

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.

Answer 1

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.

2)(1/2x^2)/(-4x)

3)-cosx

4)5secx + c

5)0

6)e^x - x^2

7) 3sinx

Answer 2

#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

#4
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) ?????