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Question

Mathematics Question on integral

∫dxcosx−sinx\displaystyle\int\frac{dx}{cosx-sinx} is equal to

A

12log⁡∣tan⁡(x2−π8)∣+C\frac{1}{\sqrt2}\log|\tan(\frac{x}{2}-\frac{\pi}{8})|+C

B

12log⁡∣cot⁡(x2)∣+C\frac{1}{\sqrt2}\log|\cot(\frac{x}{2})|+C

C

12log⁡∣tan⁡(x2−3π8)∣+C\frac{1}{\sqrt2}\log|\tan(\frac{x}{2}-\frac{3\pi}{8})|+C

D

12log⁡∣tan⁡(x2+3π8)∣+C\frac{1}{\sqrt2}\log|\tan(\frac{x}{2}+\frac{3\pi}{8})|+C

Answer

12log⁡∣tan⁡(x2+3π8)∣+C\frac{1}{\sqrt2}\log|\tan(\frac{x}{2}+\frac{3\pi}{8})|+C

Explanation

Solution

The correct option is (D): 12log⁡∣tan⁡(x2+3π8)∣+C\frac{1}{\sqrt2}\log|\tan(\frac{x}{2}+\frac{3\pi}{8})|+C