Advertisements
Advertisements
प्रश्न
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Advertisements
उत्तर
Let `"I" = int cos("x + a")/sin("x +b")"dx".` Then
`"I" = cos("x"+"b"+"a" -"b")/sin("x+b")"dx"`
`"I" = int cos{("x+b")+ ("a"- "b")}/sin("x+b")"dx"`
`"I" = int (cos("x+b").cos("a"-"b")-sin("x+b").sin("a"-"b"))/sin("x+b")"dx"`
`"I" = int [cos("a"-"b") . cot ("x+b") - sin("a"-"b")]"dx"`
`"I" = cos("a"-"b") . log |sin("x + b")| - "x".sin("a" - "b")`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
tan3 2x sec 2x
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int "dx"/(sin^2x cos^2x)` is equal to ______.
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int sqrt(1 + sinx)"d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
`int sinx/(3 + 4cos^2x) "d"x` = ______.
