Grade 12Integral Calculus
Integrate the following and please simplify Tan^3 2x sec 2xdx
1 Answer
Arun
Approved Tutor Answer8 Years agoWrite tan3(2x) as tan2(2x).tan(2x) = [sec2(2x)-1].tan(2x)
Now the function is :
Integral [sec2(2x)-1] . tan(2x) . sec(2x)dx
Put sec(2x) = u
sec(2x).tan(2x).dx = du/2
Integral [u2-1]/2
= u3/6 - u/4 + C
= sec3(2x)/6 - sec(2x)/4 + C
Now the function is :
Integral [sec2(2x)-1] . tan(2x) . sec(2x)dx
Put sec(2x) = u
sec(2x).tan(2x).dx = du/2
Integral [u2-1]/2
= u3/6 - u/4 + C
= sec3(2x)/6 - sec(2x)/4 + C
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