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Evaluate: int(-pi/2)^(pi/2)log((a-sin th...

Evaluate: `int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0`

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  2. If f(x)=int0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a)f(x)+f...

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  3. Evaluate: int(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a ...

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  4. Evaluate: int(0)^1(dx)/(1+x^2)

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  5. If f(t) is an odd function, then prove that varphi(x)=inta^xf(t)dt is ...

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  6. Evaluate: int2^3(2x^5+x^4-2x^3+2x^2+1)/((x^2+1)(x^4-1))dx

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  7. Find the value of int(0)^(1){(sin^(-1)x)//x}dx.

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  8. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive int...

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  9. Find I=int0^pi ln(1+cosx)dx

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  10. The value of inta^b(x-a)^3(b-x)^4dx is

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  11. Evaluate: int(-1/2)^(1/2)[((x+1)/(x-1))^2+((x-1)/(x+1))^2-2]^(1/2)dx

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  12. The value of int(-a)^a(cos^(- 1)x-sin^(- 1)sqrt(1-x^2))dx is (a>0) t...

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  13. If f is an odd function, then evaluate I=int(-a)^a(f(sinx)dx)/(f(cosx...

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  14. Evaluate : int0^(pi/4)log(1+tanx)dx.

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  15. Evaluate: int(-pi/4)^(pi/4)(x^9-3x^5+7x^3-x+1)/(cos^2x)dx

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  16. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

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  17. Evaluate: int(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}...

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  18. If Un=int0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zer...

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  19. Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx

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