[" Q.13The value of the integral "],[qquad int_(0)^( pi/2)(3sqrt(cos theta))/((sqrt(cos theta)+sqrt(sin theta))^(5))d theta]

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" The value of the integral "int_(0)^( pi/2)(12sqrt(cos theta))/((sqrt(cos theta)+sqrt(sin theta))^(5))d theta" equals "...

int _(0)^(pi//2) (2sqrt(cos theta))/(3(sqrt(sin theta )+ sqrt(cos theta ))) d theta is equal to

int_(0)^( pi)(sin theta+cos theta)/(sqrt(1+sin2 theta))d theta

int(sin^(3)theta)/(sqrt(cos theta))d theta

int(sqrt(cos2 theta))/(sin theta)d theta=

int(sin theta+cos theta)/(sqrt(1+sin2 theta))d theta

Evaluate: int_(0)^( pi/2)sqrt(cos theta)sin^(3)theta d theta

int (sin theta + cos theta)/(sqrt(sin 2 theta) ) d theta =