InterviewSolution
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InterviewSolution
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`int(x^(2)+cos^(2)x)/(x^(2)+1)."cosec"^(2)xdx` is equal toA. `cotx +cot^(-1)x+C`B. `-e^(ln tan^(-1))x-cot x+C`C. `C-cotx+cot^(-1)x`D. `-tan^(-1)x-("cosec x")/(sec x)+C` |
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Answer» Correct Answer - C `l=int(x^(2)+cos^(2)x)/(x^(2)+1)."cosec"^(2)xdx` `=int(x^(2)+1+cos^(2)x-1)/(x^(2)+1)."cosec"^(2)xdx` `=int(1-(sin^(2)x)/(x^(2)+1))."cosec"^(2)xdx` `=int("cosec"^(2)x-(1)/(x^(2)+1))dx` `=-cotx - tan^(-1)x+C_(1)=-cot x+cot^(-1)x-(pi)/(2)+C_(1)` `=-cotx+cot^(-1)x+C" where, "C=C_(1)-(pi)/(2)` |
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