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intsqrt(e^x-1)dxi se q u a lto 2[sqrt(...

`intsqrt(e^x-1)dxi se q u a lto` `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c` `sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)+c` `sqrt(e^x-1)+tan^(-1)sqrt(e^x-1)+c` `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c`

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int sqrt(e^(x)-1)dx is equal to

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

int(sqrt(x-1))/(xsqrt(x+1))dxi se q u a lto ln|x-sqrt(x^2-1)|-tan^(-1)x+c ln|x+sqrt(x^2-1)|-tan^(-1)x+c ln|x-sqrt(x^2-1)|-sec^(-1)x+c ln|x+sqrt(x^2-1)|-sec^(-1)x+c

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

intsqrt((e^x+1)/(e^x-1))dx (A) ln (e^(x)+sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (B) ln(e^(x)+sqrt(e^(2x)-1))+sec^(-1)(e^(x))+C (C) ln (e^(x)-sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (D) ln(e^(x)+sqrt(e^(2x)-1))-sin^(-1)(e^(-x))+C

intsqrt(1+cos e cx)dx e q u a l s 2sin^(-1)sqrt(sinx)+c (b) sqrt(2)cos^(-1)sqrt(cosx)+c c-2sin^(-1)(1-2sinx) cos^(-1)(1-2sinx)+c

Prove that (tan^(-1)(1/e))^(2)+(2e)/(sqrt(e^(2)+1) lt (tan^(-1) e)^2 + (2)/(sqrt(e^(2)+1)

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

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

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (...

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  2. int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1...

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  3. intsqrt(e^x-1)dxi se q u a lto 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c ...

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  4. If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x...

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  5. If I=int(sinx+sin^3x)/(cos2x)dx=Pcosx+Qlog|f(x)|+R , then (a)P=1/2,Q...

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  6. If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C and F(x)=int(e^x)...

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  7. Evaluate: int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)

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  8. Evaluate: int(x^3+3x+2)/((x^2+1)^2(x+1))dx

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  9. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c (b...

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  10. int((x+2)/(x+4))^2 e^xdx is equal to

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  11. IfI=int(sin2x)/((3+4cosx)^3)dx ,t h e nIe q u a l s (a)(3cosx+8)/((...

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  12. If I=int (dx)/(secx + cosec x), then equals

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  13. int(x^3dx)/(sqrt(1+x^2)) is equal to (A) 1/3sqrt(1+x^2)(2+x^2)+C ...

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  14. inte^(tanx)(secx-sinx)dx"is equal to"

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  15. 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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  16. intxsinxsec^3xdx" is equal to

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  17. 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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  18. 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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  19. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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

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