Integration final answers

Question

Answer 1

The function is .

Re-write the function.

Multiply and divide the function with

Consider .

Apply derivative on each side.

Substitute and .

Substitute

.

Therefore .

 

Consider ln|sec(x)+tan(x)|+C.

Re-write sec(x) = 1/cos(x) and tan(x)=sin(x)/cos(x)

We know that sin(x) = cos(π/2-x) and cos(x) = sin(π/2-x).

We know that then .

We know that then .

Cancel the common terms.

We know that cot(x) = tan(π/2-x).

Therefore .