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Intergrate : (sin^6x+cos^6x/sin^2x cos^2x)

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Solution: We have,

$\ I=int 1-3sin^xcdot cos^2x/sin^2xcdot cos^2xhspace0.1cmdx\ \Rightarrow I=int (1/sin^2xcdot cos^2x)dx-int 3cdot dx\ \Rightarrow I=int (sin^2x+cos^2x/sin^2xcdot cos^2x)dx-3x+c\ \Rightarrow I=int sec^2xdx+int cosec^2xdx-3x+c$

$\Rightarrow I=tanx-cotx-3x+c$

Posted by

Deependra Verma

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