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Integrate: 1/cos^3x (2sin2x)^1/2

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Solution:

$\Rightarrow I=int (1/cos^3xsqrt2sin2x)dx$

$\ Rightarrow I=1/2int dx/cos^3xsqrtsinxsqrtcosx\ \Rightarrow I=1/2int (1+tan^2x) imes sec^2x/sqrttanxhspace0.1cmdx$

put $tanx=tRightarrow sec^2xhspace0.1cmdx=dt$

$herefore$ $I=1/2int (t^-1/2+t^3/2)dt=t^1/2+1/5(t^5/2)+c$

$\Rightarrow I= an ^1/2x+(1/5) an ^5/2x+c$

Posted by

Deependra Verma

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