MHT CET 2026 Mathematics question

(A)log (cos x) + cos x + c, where c is the constant of integration
(B)log (sin x) – sin x +c, where c is the constant of integrationCorrect
(C)log (sin x) + sin x + c, where c is the constant of integration
(D)log (cos x) - cos x + c, where c is the constant of integration

Answer: (B)

Solution

Write and put , . Then \int\frac{(1-t^2)}{t^2+t}dt=\int\frac{(1-t)(1+t)}{t(t+1)}dt=\int\frac{1-t}{t}dt=\int\left(\frac1t-1\right)dt=\log t-t+c. Hence the integral is , option (B). Differentiating

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Question ID VK-099431