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int(sqrt(x-1))/(xsqrt(x+1))dxi se q u a ...

`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`

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int x(ln(x+sqrt(1+x^2))/sqrt(1+x^2)dx

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

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

The value of integral inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi se q u a lto e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))-1/(sqrt((1+x^2)^3)))+c e^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))+c none of these

Let f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2)); x in R, then

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

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x^2))+bx+c then

int1/(1+sqrt(x))"dx" is equal to a. 2sqrt(x)+2ln|1+sqrt(x)|+c b. 2sqrt(x)-2ln|1+sqrt(x)|+c c. 2sqrt(x)-2ln|1-sqrt(x)|+c d. 2sqrt(x)-ln|1+sqrt(x)|+c

int1/(1+sqrt(x))"dx" is equal to 2sqrt(x)+2ln|1+sqrt(x)|+c b. 2sqrt(x)-2ln|1+sqrt(x)|+c c. 2sqrt(x)-2ln|1-sqrt(x)|+c d. 2sqrt(x)-ln|1+sqrt(x)|+c

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: int(x^2-1)/(xsqrt((x^2+alphax+1)(x^2+betax+1)))dx

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  2. Evaluate: int(e^(tan^(-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)(...

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

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  4. IfI=int(dx)/((2a x+x^2)^(3/2)),then I is equal to (a)-(x+a)/(sqrt(2a ...

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  5. If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) ...

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  6. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dxi se q u a lto e^xtan(pi/4-x)...

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  7. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

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  8. Ifint(dx)/((x+2)(x^2+1))=aln(1+x^2)+btan^(-1)x+1/5ln|x+2|+C Then (a) ...

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  9. If int (3sinx+2cosx)/ (3cosx+2sinx) dx=a x+b ln|2sinx+3cosx|+C, then (...

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  10. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

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  11. intsqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to (a) -2/3sin^(-1)(cos...

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  12. If l^(prime)(x) means logloglog x , the log being repeated r times, th...

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  13. int(cos4x-1)/(cotx-tanx)dx is equal to (A) 1/2ln|sec2x|-1/4cos^2 2x+...

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  14. If int(dx)/(sqrt(sin^3xcos^5x))=asqrt(cotx)+bsqrt(tan^3)x+c , then (...

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  15. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  16. int(x^9dx)/((4x^2+1)^6) is equal to (a)1/(5x)(4+1/(x^2))^(-5)+c (b...

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  17. int(2sinx)/(3+sin2x)dx is equal to

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  18. int(ln(tanx)/(sinxcosx)dxi se q u a lto (a)1/2ln(tanx)+c (b) 1/2l...

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  19. intsin^(-1)((2x)/(1+x^2))dx is e q u a lto

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  20. If int(1-x^(7))/(x(1+x^(7)))dx=alog(e)|x|+blog(e)|x^(7)+1|+c, then

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