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Question

Mathematics Question on integral

∫dxx2+2x+2∫\frac{dx}{x^2+2x+2} equals

A

xtan−1(x+1)+Cx tan^{-1} (x+1)+ C

B

tan−1(x+1)+Ctan^{-1} (x+1)+ C

C

(x+1)tan−1x+C(x+1) tan^{-1} x + C

D

tan−1x+Ctan^{-1} x + C

Answer

tan−1(x+1)+Ctan^{-1} (x+1)+ C

Explanation

Solution

The correct answer is [tan−1(x+1)]+C [tan^{-1}(x+1)]+C
∫dxx2+2x+2=∫dx(x2+2x+1)+1∫\frac{dx}{x^2+2x+2} = ∫\frac{dx}{(x^2+2x+1)}+1
=∫1(x+1)2+(1)2dx= ∫\frac{1}{(x+1)^2+(1)^2} dx
=[tan−1(x+1)]+C= [tan^{-1}(x+1)]+C
Hence, the correct Answer is B