Evaluate the integral. (Remember to use ln(|u|) where appropriate.

Calculus
Tutor: None Selected Time limit: 1 Day

Use C for the constant


t sec^2 2t dt
Mar 4th, 2015

integral of t sec² 2t dt : 


Just use an integration by parts : 

f = t ⇨ df = dt 

dg = sec² 2t dt ⇨ g = (1/2) tan 2t 

⇔ 

integral of t sec² 2t dt = (1/2) t tan 2t - (1/2) integral of tan 2t dt 

u = 2t ⇨ du = 2 dt 


As integral of tan u = - ln (cos (u)), you get : 


integral of t sec² 2t dt = (1/4) ln (cos (u)) + (1/2) t tan 2t + constant 

integral of t sec² 2t dt = (1/2) t tan 2t + (1/4) ln (cos (2t)) + constant 

integral of t sec² 2t dt = (1/4) (2t tan 2t + ln (cos (2t))) + constant ⇦ answer 

Mar 4th, 2015

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