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Question
The value of `intsinx/(sinx - cosx)dx` equals ______.
Options
`1/2x + 1/2log(sinx - cosx) + C`
`1/2x - 1/2log(sinx - cosx) + C`
x + log(sinx + cosx) + C
x – log(sinx + cosx) + C
MCQ
Fill in the Blanks
Solution
The value of `intsinx/(sinx - cosx)dx` equals `underlinebb(1/2x + 1/2log(sinx - cosx) + C)`.
Explanation:
I = `1/2int(2sinx)/(sinx - cosx)dx`
= `1/2int((sinx - cosx) + (sinx + cosx))/(sinx - cosx)dx`
= `1/2int[1 + (sinx + cosx)/(sinx - cosx)]dx`
= `1/2x + 1/2log(sinx - cosx) + C`
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