Thread: Is this correct? solving integrals

Question:
∫dt/(cos^2tsqarrt(1+tant)

Mywork:
sqrt(1+tan(t)) = (1+tan(t))^(1/2)
let u = (1+tan(t))^(1/2)
du = (1/2) (1+tan(t))^(-1/2) sec^2(t) dt
du = 1/2 (1+tan^2(t))^(1/2) cos^2(t) dt
du = 1/2 sqrt(1+tan^2(t)) cos^2(t) dt
The given integral becomes
2∫ du
=2u + C
= 2sqrt(1+tan^2(t)) + C

Originally Posted by kensington

Question:
∫dt/(cos^2tsqarrt(1+tant)

Mywork:
sqrt(1+tan(t)) = (1+tan(t))^(1/2)
let u = (1+tan(t))^(1/2)
du = (1/2) (1+tan(t))^(-1/2) sec^2(t) dt
du = 1/2 (1+tan^2(t))^(1/2) cos^2(t) dt

Be careful here- you mean 1/2((1+ tan^2(t))^(1/2)(cos^2(t))) don't you?
That is, and not , which is what you wrote.

du = 1/2 sqrt(1+tan^2(t)) cos^2(t) dt
The given integral becomes
2∫ du
=2u + C
= 2sqrt(1+tan^2(t)) + C

With my comment, yes, that is correct.