int(0)^(2)xsqrt(2-x)dx=(16sqrt(2))/(15)...

`int_(0)^(2)xsqrt(2-x)dx=(16sqrt(2))/(15)`

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int(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(pi^(2))/(2ab)
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int(0)^(pi)(xsinxdx)/(1+cos^(2)x)=(pi^(2))/(4)
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int(0)^((pi)/(2))(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)
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int(0)^(pi)xsinxcos^(2)xdx=(pi)/(3)
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int(0)^((pi)/(2))(cos^(2)thetad theta)/(sintheta+costheta)=(1)/(sqrt(2...
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int(0)^((pi)/(2))sin2xlog(tanx)dx=0
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int(0)^(pi)(xtanxdx)/(tanx+secx)=(pi)/(2)(pi-2)
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int(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)
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int(0)^(1.5)[x^(2)]dx=2-sqrt(2)
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int(0)^(2a)(f(x)dx)/(f(x)+f(2a-x))=a
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int(a)^(b)(f(x)dx)/(f(x)+f(a+b-x))=(1)/(2)(b-a)
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int(0)^(1)log((1-x)/(x))dx=0
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int(1)^(2)(sqrt(x)dx)/(sqrt(x)+sqrt(3-x))=(1)/(2)
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int((pi)/(6))^((pi)/(3))(dx)/(1+sqrt(tanx))=(pi)/(12)
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int(-a)^(a)sqrt((a-x)/(a+x))dx=api
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int(0)^(2)xsqrt(2-x)dx=(16sqrt(2))/(15)
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int(0)^((pi)/(2))log(sinx)dx=int(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log....
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