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प्रश्न
`int (sin^8x - cos^8x)/(1 - 2sin^2x cos^2x) dx` is equal to
विकल्प
`1/2 sin 2x + C`
`-1/2 sin 2x + C`
`- 1/2 sin x + C`
`- sin^2x + C`
MCQ
उत्तर
`-1/2 sin 2x + C`
Explanation:
I = `int (sin^8x - cos^8x)/(1 - 2sin^2x cos^2x)`
= `int((sin^4x - cos^4x)(sin^4x + cos^4x))/(1 - 2sin^2x cos^2x) dx`
= `int ((sin^2x - cos^2x)(sin^2x + cos^2x)(sin^4x + cos^4x))/(1 - 2sin^2xcos^2x) dx`
= `int (1.(sin^2x - cos^2x)[(sin^2x + cos^2x)^2 - 2sin^2x cos^2x])/(1 - 2sin^2x cos^2x)`
= `int ((sin^2x - cos^2x)(1 - 2sin^2x cos^2x))/(1 - 2sin^2x cos^2x) dx`
= `- int cos 2x dx`
= `- 1/2 sin 2x + C`
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