Description : Integral [x^3 + 1]^2 dx = ? I found that it was [(x^3 + 1)^3] / 9x^2, but that is wrong? Details inside.
Last Answer : Expand this using FOIL. You will get three distinct terms and it will be a very easy integral. The answer should be (x^7)/7 + (x^4)/2 + x
Description : What is the integral of xe^(-x) dx?
Last Answer : Sorry, my fingers and toes only go to 20.
Description : Evaluate the following integral: `int_1^3(cos(logx))/x dx`
Last Answer : Evaluate the following integral: `int_1^3(cos(logx))/x dx`
Description : The value of definite integral `int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx` is
Last Answer : The value of definite integral `int_(-pi)^(pi) (cos 2x. cos2^(2)x.cos2^(3)x.cos 2^(4)x.cos2^(5)x)dx` is A. 1 B. `-1` C. 0 D. 2
Description : Evaluate the following integral : ∫sin x dx, x∈(π/2, 0)
Last Answer : Evaluate the following integral : (i) \(\int_0^{\pi/2}\,sin\,x\,dx\) ∫sin x dx, x∈(π/2, 0) (ii) \(\int_1^5\,x\,dx\) ∫ x dx, x∈(5, 1)
Description : `int (4x^(2) +x+1)/(x^(3) -1) dx=?`
Last Answer : `int (4x^(2) +x+1)/(x^(3) -1) dx=?` A. `log (x-1) -log (x^(3) -1) +c` B. `log (x^(3) -1) +log (x-1)+c` C. None of the above D.
Description : `int (x^(2))/((a+bx)^(2))dx=?`
Last Answer : `int (x^(2))/((a+bx)^(2))dx=?` A. `(-x^(2))/(b(a+bx))+(2)/(b^(2)) [x-(a)/(b) log (a+bx)]+c` ... ^(2)) [x-(a)/(b)log (a+bx)]+c` C. None of the above D.
Description : Evaluate: `int((x-1)e^x)/((x+1)^3)dx`
Last Answer : Evaluate: `int((x-1)e^x)/((x+1)^3)dx` A. `(e^(x))/((x+1)^(2))+c` B. `(e^(x))/((x+1)^(3))+c` C. `(e^(x))/((x+1)^(4))+c` D.
Description : `int (1-sinx )/ (1-cos x) dx=?`
Last Answer : `int (1-sinx )/ (1-cos x) dx=?` A. `cot .(x)/(2) -2 log sin .(x)/(2) +c` B. `-cot .(x)/(2) -2 log sin .(x)/(2) +c` C. None of the above D.
Description : `int log (x^(2) +a^(2)) dx=?`
Last Answer : `int log (x^(2) +a^(2)) dx=?` A. `x log (x^(2)+a^(2)) -2x +2a tan^(-1).(x)/(a)+c` B. `x log ... 2x -2a tan^(-1) . (x)/(a) +c` C. None of the above D.
Description : `int {1+2 tan x (tan x + sec x )}^(1//2) dx=?`
Last Answer : `int {1+2 tan x (tan x + sec x )}^(1//2) dx=?` A. `log {cosec x(sec x+tan x)}+c` B. `log {sec x (sec x+ tan x)} +c` C. None of the above 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 (x)/( 1+cos x) dx=?`
Last Answer : `int (x)/( 1+cos x) dx=?` A. `x tan (x)/(2) + 2 log cos (x)/(2) + c` B. ` x tan (x)/(2) + 2 log sin (x)/(2)+c` C. None of the above D.
Description : `int sin^(3) x cos^(3) x dx =?`
Last Answer : `int sin^(3) x cos^(3) x dx =?` A. `(1)/(4) sin^(4) x + (1)/(6) sin^(6) x+c` B. `(1)/(4) cos^(4)x-(1)/(6) cos^(6) x+c` C. none of the above D.
Description : `int(sin(x-alpha)/(sin(x+alpha)) dx`
Last Answer : `int(sin(x-alpha)/(sin(x+alpha)) dx` A. `x cos 2alpha +sin 2alpha log| sin (x+alpha)|+c` B. `x cos ... log |sin (x+alpha)|+c` C. None of the above D.
Description : `int (e^(m tan^(-1) x))/(1+x^(2)) dx=?`
Last Answer : `int (e^(m tan^(-1) x))/(1+x^(2)) dx=?` A. `(1)/(m) e^(m tan^(-1)x) +c` B. `e^(m tan^(-1)x) +c` C. None of these D.
Description : `int(tan^(-1)x)/(1+x^(2)) dx=?`
Last Answer : `int(tan^(-1)x)/(1+x^(2)) dx=?` A. `(1)/(3) (tan^(-1) x)^(2)+c` B. `(tan^(-1) x)^(2) +c` C. `(tan^(-1) x)^(3) +c` D.
Description : `int (x^(2))/(x^(2) +4) dx=?`
Last Answer : `int (x^(2))/(x^(2) +4) dx=?` A. `x+4 tan^(-1) ((x)/(2))+c` B. `x-2 tan^(-1) ((x)/(2))+c` C. None of the above D.
Description : `int (1-cos x)/(1+cos x) dx=?`
Last Answer : `int (1-cos x)/(1+cos x) dx=?` A. `2 tan ((x)/(2))+ x+c` B. ` tan ((x)/(2)) + x+c` C. `tan ((x)/(2)) + 2x + c` D. none of these
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 (1)/(sin^(2) x cos^(2)x) dx=?`
Last Answer : `int (1)/(sin^(2) x cos^(2)x) dx=?` A. `tan x-cot x+c` B. `sec x+ cosec x+c` C. `sec x- cosec x+c` D.
Description : ` int (3-4 sin x)/(cos^(2) x) dx=?`
Last Answer : ` int (3-4 sin x)/(cos^(2) x) dx=?` A. `4 tan x +4 sec x+c` B. ` 3 tan x + 4 sec x+ c` C. ` 4 tan x +3 sec x+c` D.
Description : Evaluate: `int(x^2-1)/(x^4+x^2+1) dx`
Last Answer : Evaluate: `int(x^2-1)/(x^4+x^2+1) dx`
Description : `int (x^2+1)/(x^4+1) dx`
Last Answer : `int (x^2+1)/(x^4+1) dx`
Description : `int(x^(2)+1)/(x^(4)-2x^(2)+1)dx`
Last Answer : `int(x^(2)+1)/(x^(4)-2x^(2)+1)dx`
Description : `int(1)/(3+4 sin x)dx`
Last Answer : `int(1)/(3+4 sin x)dx`
Description : `int(x^2+1)/(x^4+x^2+1)`dx
Last Answer : `int(x^2+1)/(x^4+x^2+1)`dx
Description : Evaluate: `int(x^2+4)/(x^4+16)dx`
Last Answer : Evaluate: `int(x^2+4)/(x^4+16)dx`
Description : `int(1)/(3+2 sin x +cos x)dx`
Last Answer : `int(1)/(3+2 sin x +cos x)dx`
Description : `int(1)/(5-4 sin x)dx`
Last Answer : `int(1)/(5-4 sin x)dx`
Description : `int(1)/(5+2 cos x)dx`
Last Answer : `int(1)/(5+2 cos x)dx`
Description : `int(1)/((sin x-2 cos x) (2 sin x+c osx))dx`
Last Answer : `int(1)/((sin x-2 cos x) (2 sin x+c osx))dx`
Description : `int(1)/(sin x cos x + 2cos^(2)x)dx`
Last Answer : `int(1)/(sin x cos x + 2cos^(2)x)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 : `int(1)/(cos^(2) x-3 sin^(2) x)dx`
Last Answer : `int(1)/(cos^(2) x-3 sin^(2) x)dx`
Description : `int(1)/(sin^(2)x-4 cos^(2)x)dx`
Last Answer : `int(1)/(sin^(2)x-4 cos^(2)x)dx`
Description : `int(1)/(3sin^(2) x+4 cos^(2) x)dx`
Last Answer : `int(1)/(3sin^(2) x+4 cos^(2) x)dx`
Description : `int(1)/(2+sin^(2) x)dx`
Last Answer : `int(1)/(2+sin^(2) x)dx`
Description : `int(1)/((asin x+b cos x)^(2))dx`
Last Answer : `int(1)/((asin x+b cos x)^(2))dx`
Description : `int(1)/((2 sin x + cos x)^(2))dx`
Last Answer : `int(1)/((2 sin x + cos x)^(2))dx`
Description : `int(1)/(1+3 cos^(2) x)dx`
Last Answer : `int(1)/(1+3 cos^(2) x)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)/((x+1)^(2)-4)dx`
Last Answer : `int (1)/((x+1)^(2)-4)dx`