`int(cosx)/((1+sinx)(2+sin x))dx`

1.	`int(cosx)/((1+sinx)(2+sin x))dx`
Answer» Correct Answer - `log\|(1+sin x)/(2+sin x)\|+C` Putting `sin x=t` and` cos x dx=dt,`we get `I=int(dt)/((1+t)(2+t)).`

Discussion

`int ((1+tanx))/((x-logcosx))dx.`
Examples: ` int sec^2x / sqrt ( 16 + tan^2x) dx`A. `log|tanx+sqrt(tan^(2)x+16)|+C`B. `log|x+sqrt(tan^(2)x+16)|+C`C. `log|tan x-sqrt(tan^(2)x+16)|+C`D. None of these
`int (x)/((x^(4)-16))dx=?`A. `(1)/(4)log |(x^(2)+4)/(x^(2)-4)+C`B. `(1)/(16)log |(x^(2)+4)/(x^(2)-4)+C`C. `(1)/(16)log |(x^(2)-4)/(x^(2)+4)+C`D. None of these
`int(x^(2))/(sqrt(x^(6)-1))dx=?`A. `(1)/(2) log |x^(3)+sqrt(x^(6)-1)|+C`B. `(1)/(3) log |x^(3)+sqrt(x^(6)-1)|+C`C. `(1)/(3) log |x^(3)-sqrt(x^(6)-1)|+C`D. None of these
Evaluate:`int(sinx)/(sqrt(4cos^2x-1))dx`A. `-(1)/(2)log |2cosx+sqrt(4cos^(2)x-1)|+C`B. `-(1)/(3)log |2cosx+sqrt(4cos^(2)x-1)|+C`C. `-(1)/(6)log |cosx+sqrt(2cos^(2)x-1)|+C`D. None of these
Evaluate:`int(3_(4x)-x^2)/((x+2)(x-1))dx`
Evaluate `int dx/(x(x^n+1))`
Evaluate: `int(2x+5)/(x^2-x-2) dx`
Evaluate: `int(x^3)/((x-1)(x-2)) dx`
Evaluate :`int(x^2)/((x^2+4)(x^2+9))dx`