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IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q...

`IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s` `1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C` `1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C` `1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C` `1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C`

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IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s a. 1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C b. 1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C c. 1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C d. 1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1))/(x^3)+C (b) (sqrt(2x^4-2x^2+1))/x+C (c) (sqrt(2x^4-2x^2+1))/(x^2)+C (d) (sqrt(2x^4-2x^2+1))/(2x^2)+C

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3sqrt(1+x^2)(x^2-1)+C 1/3(1+x^2)^(3/2)+C (d) 1/3sqrt(1+x^2)(x^2-2)+C

y= tan^(-1)(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)) then dy/dx

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

If I=intdx/(x^4sqrt(a^2+x^2)),t h e nI equals 1/(a^4)[1/xsqrt(a^2+x^2)-1/(3x^3)sqrt(a^2+x^2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)-1/(3x^3)(a^2+x^2)^(3//2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)-1/(2sqrt(x))(a^2+x^2)^(3//2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)+1/(3x^3)sqrt(a^2+x^2)]+c

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. int e^x((x^2+1))/((x+1)^2)dx is equal to ((x-1)/(x+1))e^x+c (b) e^x(...

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  2. intxsinxsec^3xdx" is equal to

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  3. IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s 1/2((sqrt(x^2-1))/(...

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  4. int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a)1/2(ln((x-1)/(x+1)...

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  5. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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  6. "Let " k(x)=int((x^(2)+1)dx)/(root(3)(x^(3)+3x+6)) " and " k(-1)=(1)/(...

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  7. Column I a) int(x^2-x+1)/(x^3-4x^2+4x)dx b) int(x^2-1)/(x(x-2)^3)dx ...

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  8. Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot The...

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  9. Each question contains statements given in two columns which have to b...

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  10. The value of ∫e^2x ( 1/x ​ − 1/(2x^2) ​ )dx is

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  11. Statement 1: If the primitive of f(x)=pisinpix+2x-4 has the value 3 fo...

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  12. Let f(x)=2^(2x−1)and ϕ(x) =−2^x+2xlog2. If f'(x)>ϕ'(x), then value of ...

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  13. Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-...

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  14. If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b...

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  15. If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(...

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  16. Evaluate: intsqrt((1-sqrt(x))/(1+sqrt(x)))dx

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  17. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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  18. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

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  19. Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value o...

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  20. If y=intsqrt(x)(1+x^(1/3))^4dx"i se q u a lto"

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