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int1/(1+sqrt(x))"dx" is equal to 2sqrt(x...

`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`

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int(1)/(1+sqrt(x))dx is equal to 2sqrt(x)+2ln|1+sqrt(x)|+c b.2sqrt(x)-2ln|1+sqrt(x)|+cc2sqrt(x)-2ln|1-sqrt(x)|+cd2sqrt(x)-ln|1+sqrt(x)|+c

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int_(1)^(2)(1)/(x sqrt(log x))dx =

int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))= (a) 1/2ln(1+sqrt(1+x^2))+c (b) 2sqrt(1+sqrt(1+x^2))+c (c) 2(1+sqrt(1+x^2))+c (d) 4sqrt(1+sqrt(1+x^2))+c

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

int ln(sqrt(1+x)+sqrt(1-x))dx

int sqrt((x)/(1-x))dx is equal to 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

RESONANCE DPP-JEE MAINS-All Questions
  1. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec ax...

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  2. Let vec a , vec b , vec c be the three unit vectors such that vec a+...

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

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  4. If ABCD is a parallelogram, vec A B=2 hat i+4 hat j-5 hat k and vec ...

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  5. If the vectors bar A B=3 hat i+4 hat k and bar A C=5 hat i-2 hat j+...

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  6. If f^(prime)(1)=-2sqrt(2)a n dg^(prime)(sqrt(2))=4 , then the derivati...

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  7. int (x^2+2)/(x^4+4) dx=

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  8. int0^pi||sinx|-|cosx||dx is equal to (a)tan((3pi)/8) (b) tan(pi...

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  9. Let f(x)={(sinx^2)/xx!=0 0x=0, then f^(prime)(0^+)+(0^-) has the value...

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  10. The equation of a line 4x-4y-z+11=0=x+2y-z-1 can be put as x/2=(y-2)/1...

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  11. If y=a t^2+2b t+c&t=a x^2+2b x+c , then (d^3y)/(dx^3) equals 24 a^2(a ...

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  12. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero ve...

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  13. If [ vec a vec b vec c]=2 and vec x=2 vec a+3 vec b+ vec c , vec y= v...

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  14. Let u=int0^1("ln"(x+1))/(x^2+1)dxa n dv=int0^(pi/2)ln(sin2x)dx ,t h e ...

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  15. int(-1/(sqrt(3)))^(1/(sqrt(3)))(cos^(-1)((2x)/(x^2+1))+tan^(-1)((2x)/(...

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  16. Find the integral value of n for which lim(x->0)(cos^2x-cosx-e^xcos...

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  17. If y=cos^(-1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2))),t h e n(dy)/(dx) i...

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  18. If vec a= hat i+ hat j+ hat k , vec b=4 hat i+3 hat j+4 hat k and ve...

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  19. 1)int(-pi/2)^pi sin^(-1) (sinx) dx 2)int(-pi/2)^(pi/2) (-pi/2)/(sqr...

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  20. if f(x) = lim(n->oo) 2/n^2(sum(k=1)^n kx)((3^(nx)-1)/(3^(nx)+1)) where...

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