Rational Integral

Question

Solve step by step.

Answer 1

Given expression :

Let x = tank

Then Apply derivative

dx = sec²k dk

Then substitute x = tank and dx = sec²k dk

Use trigonometric identity : sec²x = 1 + tan²x

Substitute seck = 1/cosk

Divide and multiply denominator with √2.

Substitute :

Apply formula : sinAcosB+cosAsinB = sin(A+B)

Substitute coseck = 1/sink

Apply formula : ⌠cosecx = - ln |cosecx+cotx| + C

Substitute tank = x

The solution is