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`int (sin^(6)x+cos^(6)x)/(sin^(2)xcos^(2)x)dx` का मान ज्ञात कीजिए |

Answer» `int(sin^(6)x+cos^(6)x)/(sin^(2)xcos^(2)x)dx`
`=int((sin^(2)x+cos^(2)x)^(3)-3sin^(2)xcos^(2)x(sin^(2)x+cos^(2)x))/(sin^(2)xcos^(2)x)dx`
`=int(1-3sin^(2)xcos^(2)x)/(sin^(2)xcos^(2)x)dx`
`=int((1)/(sin^(2)xcos^(2)x)-3)dx=int((sin^(2)x+cos^(2)x)/(sin^(2)xcos^(2)x-3))dx`
`=int(sin^(2))/(sin^(2)xcos^(2)x)dx+int(cos^(2)x)/(sin^(2)xcos^(2)x)dx-3intdx`
`=int(1)/(cos^(2)x)dx+int(1)/(sin^(2)x)dx-3intdx`
`=intsec^(2)xdx+intcosec^(2)xdx-3intdx`
`=tanx-cotx-3x+c`


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