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e power tan inverse x. (1+x+x sqr) / (1+x sqr)

e power tan inverse x. (1+x+x sqr) / (1+x sqr)

Grade:12th pass

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
integral e power tan inverse x .(1+x+x^2)/(1+x^2) dx
let tan inverse x =t => x+tan t
Differentiating w. r . x.
1/(1+x^2) dx= dt
integral e power t ( 1+tan t +tan ^2 t)dt
integral e power t ( tan t + sec^2t) dt
integral e^t.tant dt+ integral e^tsec^2tdt
on integrating second integral we get
integral e^t.tan t dt+ e^t.tant- integral e^t.tant dt
e^t.tant +c
e^tan inverse x .x + c
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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