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a
13x+x2+132−x+x2+1−12+C
b
12x+x2+112−x+x2+1−12+C
c
13x−x2+132−x+x2+112+C
d
13x+x2+132+x+x2+1−12+C
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Correct option is A
Let I=∫x+x2+1dx Let x+x2+1=t….(1) Rationalize ⇒x2+1−x=1t….(2) Subtract (1) &(2)⇒2x=t−1t⇒x=12t−1tDifferentiating with respect to x on both sidesdx=121+1t2dt∴I=12∫t12+t−32dt=13t32−t−12+C , where t= x+x2+1Similar Questions
is equal to
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