Advertisements
Advertisements
Question
Find :
`∫ sin(x-a)/sin(x+a)dx`
Advertisements
Solution
`∫ sin(x-a)/sin(x+a)dx`
`I = ∫ sin(x-a)/sin(x+a)dx`
= `∫sin(x-a+a-a)/sin(x+a)dx`
= `∫sin(x+a-2a)/sin(x+a)dx`
= `∫(sin(x+a) cos2a - sin 2acos(x+a))/sin(x+a)dx`
= `∫ cos 2a dx - ∫ sin 2acot(x+a)dx`
`I = x cos 2a - sin 2a log |sin(x+a)|+C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`2/((1-x)(1+x^2))`
`int (xdx)/((x - 1)(x - 2))` equals:
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`
Integrate the following w.r.t. x : `2^x/(4^x - 3 * 2^x - 4`
Integrate the following w.r.t. x : `(1)/(2sinx + sin2x)`
Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`
Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`
Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int sqrt((9 + x)/(9 - x)) "d"x`
`int ("d"x)/(x^3 - 1)`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
State whether the following statement is True or False:
For `int (x - 1)/(x + 1)^3 "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
`int 1/(x^2 + 1)^2 dx` = ______.
If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1 x/2 + B tan^-1(x/3) + C`, then A – B = ______.
What is the result of dividing \[x^{2}+1\] by \[x^{2}-5x+6\]?
For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?
What numerator should be used for each distinct linear factor in a partial-fraction decomposition?
