Description : Evaluate `int_0^(pi/4)(sqrt(tanx)+sqrt(cotx))dx`
Last Answer : Evaluate `int_0^(pi/4)(sqrt(tanx)+sqrt(cotx))dx` A. `-(pi)/(sqrt(2))` B. `(pi)/(2)` C. `-(pi)/(2)` D.
Description : integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`
Last Answer : integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`
Description : prove that `int_0^oo x^2/((x^2+a^2)(x^2+b^2))dx=pi/(2(a+b))`
Last Answer : prove that `int_0^oo x^2/((x^2+a^2)(x^2+b^2))dx=pi/(2(a+b))`
Description : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx`
Last Answer : Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx` A. `(pi(a^(2) +b^(2)))/(4a^(3)b^(3))` B. ` ... )+b^(2)))/(4a^(2)b^(2))` C. None of the above D.
Description : Prove that: `int_0^(pi//2)log|tanx+cotx|dx=pi(log)_e2`
Last Answer : Prove that: `int_0^(pi//2)log|tanx+cotx|dx=pi(log)_e2` A. `-pi log 2` B. `pi log 2` C. `(pi)/(2) log 2` D.
Description : `int_(0)^(pi//4) sqrt(cot x dx) =?`
Last Answer : `int_(0)^(pi//4) sqrt(cot x dx) =?` A. `(Pi sqrt(2))/(4)+(1)/(sqrt(2)) log (sqrt(2)-1)` B. `(- ... (pisqrt(2))/(4) -(1)/(sqrt(2))log (sqrt(2)-1)` D.
Description : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?`
Last Answer : `int_(0)^(1//2) (x sin^(-1)x)/(sqrt(1-x^(2)))dx=?` A. `(pi sqrt(3))/(12)+(1)/(2)` B. `(pisqrt(3))/(12)-(1)/(2)` C. `(pisqrt(3))/(12) -(1)/(2)` D.
Description : `int (1)/(sqrt(sin^(3) x cos x))dx =?`
Last Answer : `int (1)/(sqrt(sin^(3) x cos x))dx =?` A. `-2sqrt(tan x) +c` B. `(2)/(sqrt(tan x)) +c` C. `(-2)/(sqrt(tan x)) +c` D.
Description : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?`
Last Answer : `int_(0)^(1) (x)/(sqrt(1+x^(2)))dx=?` A. `sqrt(2)-1` B. `sqrt(2)` C. `-sqrt(2)` D.
Description : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?`
Last Answer : `int_(0)^(1) sqrt((1-x)/(1+x)) dx=?` A. `(pi)/(2)+1` B. `(pi)/(2) -1` C. None of these D.
Description : `int(sin x)/( sqrt(1+cos x))dx=?`
Last Answer : `int(sin x)/( sqrt(1+cos x))dx=?` A. `sqrt(1+cos x) +c` B. `-2sqrt(1+ cos x)+c` C. `2sqrt(1+ cos x) +c` D.
Description : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Last Answer : `int_(0)^(1) x sqrt((1-x^(2))/(1+x^(2)))dx`
Description : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Last Answer : `int_(0)^(2) sqrt((2+x)/(2-x)) dx`
Description : `int_(0)^(1//sqrt(2)) (sin^(-1))/((1-x^(2))^(3//2))dx`
Last Answer : `int_(0)^(1//sqrt(2)) (sin^(-1))/((1-x^(2))^(3//2))dx`
Description : `int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx`
Last Answer : `int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx`
Description : `int_(0)^(1) (x sin^(-1)x)/(sqrt(1+2x)^(2))dx`
Last Answer : `int_(0)^(1) (x sin^(-1)x)/(sqrt(1+2x)^(2))dx`
Description : `int_(0)^(a) (x)/(sqrt(a^(2)-x^(2)))dx`
Last Answer : `int_(0)^(a) (x)/(sqrt(a^(2)-x^(2)))dx`
Description : `int_(a)^(2a) (sqrt((a)/(x))+sqrt((x)/(a)))^(2)dx`
Last Answer : `int_(a)^(2a) (sqrt((a)/(x))+sqrt((x)/(a)))^(2)dx`
Description : `int_(0)^(1) (1)/(sqrt(1-x^(2)))dx`
Last Answer : `int_(0)^(1) (1)/(sqrt(1-x^(2)))dx`
Description : `int(x)/(sqrt(x^(2)+x+1))dx`
Last Answer : `int(x)/(sqrt(x^(2)+x+1))dx`
Description : `int(2x+5)/(sqrt(x^(2)+3x+1))dx`
Last Answer : `int(2x+5)/(sqrt(x^(2)+3x+1))dx`
Description : `int(x+1)/(sqrt(2x^(2)+x-3))dx`
Last Answer : `int(x+1)/(sqrt(2x^(2)+x-3))dx`
Description : Evaluate: `int(2x+5)/(sqrt(x^2+2x+5)) dx`
Last Answer : Evaluate: `int(2x+5)/(sqrt(x^2+2x+5)) dx`
Description : `int(1)/(sqrt(x^(2)|3x|d1))dx`
Last Answer : `int(1)/(sqrt(x^(2)|3x|d1))dx`
Description : Evaluate: `int(2x-5)sqrt(2+3x-x^2)dx`
Last Answer : Evaluate: `int(2x-5)sqrt(2+3x-x^2)dx`
Description : Evaluate: `int(4x+1) sqrt(x^2-x-2) dx`
Last Answer : Evaluate: `int(4x+1) sqrt(x^2-x-2) dx`
Description : Evaluate: `int(x-5) sqrt(x^2+x) dx`
Last Answer : Evaluate: `int(x-5) sqrt(x^2+x) dx`
Description : `int(x+2)sqrt(x^(2)+x)dx`
Last Answer : `int(x+2)sqrt(x^(2)+x)dx`
Description : `int(1)/(sqrt(1+x-x^(2)))dx`
Last Answer : `int(1)/(sqrt(1+x-x^(2)))dx`
Description : `int(1)/(sqrt(4x^(2)-x+4))dx`
Last Answer : `int(1)/(sqrt(4x^(2)-x+4))dx`
Description : ` int sec x tan x sqrt(sec^(2) x+1)dx`
Last Answer : ` int sec x tan x sqrt(sec^(2) x+1)dx`
Description : `int (x^(2) +1)/(sqrt(x^(2)+3))dx`
Last Answer : `int (x^(2) +1)/(sqrt(x^(2)+3))dx`
Description : `int sec x tan x sqrt(tan^(2) x-4) dx`
Last Answer : `int sec x tan x sqrt(tan^(2) x-4) dx`
Description : Evaluate: (i) `int(e^x)/(sqrt(4-e^(2x))) dx` (ii) `int(x^2)/(sqrt(1-x^6)) dx`
Last Answer : Evaluate: (i) `int(e^x)/(sqrt(4-e^(2x))) dx` (ii) `int(x^2)/(sqrt(1-x^6)) dx`
Description : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx`
Last Answer : `(i) int(2cos x)/(sqrt(1-4cos^(2) x))dx " "(ii) int (x+1)/(sqrt(x^(2)+1))dx`
Description : `(i) int(sinx)/(sqrt(4+ cos^(2) x)) dx " "(ii) int(x^(2))/(sqrt(9+x^(6)))dx`
Last Answer : `(i) int(sinx)/(sqrt(4+ cos^(2) x)) dx " "(ii) int(x^(2))/(sqrt(9+x^(6)))dx`
Description : `int(1)/(sqrt(x^(2) -9))dx`
Last Answer : `int(1)/(sqrt(x^(2) -9))dx`
Description : `(i) int(1)/(sqrt(1-x^(2)).cos^(-1) x)dx` `(ii) int (sin(tan^(-1)x))/(1+x^(2))dx`
Last Answer : `(i) int(1)/(sqrt(1-x^(2)).cos^(-1) x)dx` `(ii) int (sin(tan^(-1)x))/(1+x^(2))dx`
Description : `int(sec^(2)x)/(sqrt(tanx))dx`
Last Answer : `int(sec^(2)x)/(sqrt(tanx))dx`
Description : `int(2x-1)/(sqrt(x^(2)-x-1))dx`
Last Answer : `int(2x-1)/(sqrt(x^(2)-x-1))dx`
Description : `int((a+bsin^(-1)x)^(n))/(sqrt(1-x^(2)))dx`
Last Answer : `int((a+bsin^(-1)x)^(n))/(sqrt(1-x^(2)))dx`
Description : `(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx`
Last Answer : `(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx`
Description : Evaluate: (i) `int(e^(sqrt(x))cos(e^(sqrt(x))))/(sqrt(x)) dx` (ii) `int(cos^5x)/(sinx) dx`
Last Answer : Evaluate: (i) `int(e^(sqrt(x))cos(e^(sqrt(x))))/(sqrt(x)) dx` (ii) `int(cos^5x)/(sinx) dx`
Description : `int (x) /(sqrt(1+x^(4)) ) dx`
Last Answer : `int (x) /(sqrt(1+x^(4)) ) dx`
Description : `int(x)/(sqrt(1+x^(2)))dx`
Last Answer : `int(x)/(sqrt(1+x^(2)))dx`
Description : `int ( x^(2))/(sqrt(1+x^(3)))dx`
Last Answer : `int ( x^(2))/(sqrt(1+x^(3)))dx`
Description : `int cosec^(2)x. sqrt(cot) dx`
Last Answer : `int cosec^(2)x. sqrt(cot) dx`
Description : `int(1)/(sqrt(5-.(x^(2))/(4)))dx`
Last Answer : `int(1)/(sqrt(5-.(x^(2))/(4)))dx`
Description : `(i) int(1)/(5x+1)dx " "(ii)int(1)/(sqrt(x+1+)sqrt(x))dx`
Last Answer : `(i) int(1)/(5x+1)dx " "(ii)int(1)/(sqrt(x+1+)sqrt(x))dx`