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Question: \(\int_{}^{}\frac{\sqrt{1–x^{2}} + \sqrt{1 + x^{2}}}{\sqrt{1–x^{4}}}\) dx =...

∫1–x2+1+x21–x4\int_{}^{}\frac{\sqrt{1–x^{2}} + \sqrt{1 + x^{2}}}{\sqrt{1–x^{4}}} dx =

A

log(x+1+x2)(x + \sqrt{1 + x^{2}}) + sin–1 x + c

B

sin h–1 x – sin–1 x + c

C

cos–1 x – sin–1 x + c

D

tan–1 x + sin–1 x + c

Answer

log(x+1+x2)(x + \sqrt{1 + x^{2}}) + sin–1 x + c

Explanation

Solution

∫1−x21−x4+1+x21−x4dx\int \frac { \sqrt { 1 - x ^ { 2 } } } { \sqrt { 1 - x ^ { 4 } } } + \frac { \sqrt { 1 + x ^ { 2 } } } { \sqrt { 1 - x ^ { 4 } } } d x= ∫dx1+x2+∫dx1–x2\int_{}^{}\frac{dx}{\sqrt{1 + x^{2}}} + \int_{}^{}\frac{dx}{\sqrt{1–x^{2}}}