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1-x 2 / (1+x 2 ) 2 where x= tan θ



1-x2 / (1+x2)2 where x= tan θ


Grade:Select Grade

2 Answers

Srikrishna Guruduth
32 Points
7 years ago

(1-tan^2Φ)/(sec^2Φ)^2 now put u=sec^2phi

apoorva sagarwal
16 Points
7 years ago

∫1-x2/(1+x2)

add and subtract 1 to numerator ,you get

∫2/(1+x2)2  dx - ∫1/(1+x2) dx  ===>  ∫2/(1+x2)2 dx-tanx+c

= let x=tanθ

===> dx=sec2θ dθ

∫2/(1+tan2θ)2  sec2θ dθ -tanx+c

=∫2cos2θ dθ-tanx+c

=(cos2θ+1)dθ-tanx+c

=sin2θ/2 +x-tanx+c

=tanθ/1+tan2θ +x-tanx+c

but x=tanθ 

x/(1+x2) +x-tanx+c 

 

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