Evaluate the Integral

Question

Evaluate  .

Question options:

1)	tan(x) + C
2)	sec2(x) + C
3)	-cot(x) + C
4)	None of these

Answer 1

cos(x)/cos^3(x) = 1/cos^2(x) = sec^2(x)

The integral of sec^2(x) can be found in integral table.

Answer 2

The quotient of cos(x) and cos³(x) reduces to 1/cos²(x). This is a reciprocal trig function that is equal to sec²(x), so then the problem becomes, "What is the integral of secant squared of x, dx?" This is a common integral that is found any table of integrals: Integral of sec²(x)dx = tan(x) +C.

Answer 3

The integral is the same as the integral of sec²(x) which is tan(x) + constant.