I'm trying to integrate: \(\displaystyle\int{\frac{{{8}{\left.{d}{x}\right.}}}{{{3}{\cos{{2}}}{x}+{1}}}}\)

Alan Zavala

Alan Zavala

Answered question

2022-04-06

I'm trying to integrate:
8dx3cos2x+1

Answer & Explanation

resacarno4u

resacarno4u

Beginner2022-04-07Added 12 answers

Notice, the steps of substitution you showed are correct but your final answer is wrong. It shouldn't be in terms of
if you let z=tanx2dx=2dz1+z2 then
8dx3cos2x+1
=8dx3(2cos2x1)+1=4dx3cos2x1
=43(1z21+z2)212dz1+z2
=4(1+z2)z44z2+1dz
=4d(z1z)(z1z)2(2)2
=422ln|z1z2z1z+2|+C

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