Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Advertisements
उत्तर
`int (3 + 4cosx)/(sin^2x) "d"x = int(3/(sin^2x) + (4cosx)/(sin^2x)) "d"x`
= `int 3/(sin^2x) "d"x + int (4cosx)/sinx * 1/sinx * "d"x`
= `3 int "cosec"^2 x "d"x + 4 int cotx "cosec" x * "d"x`
= `3 int "cosec"^2x "d"x + 4 int "cosec" x cotx "d"x`
= 3 × – cot x + 4 × – cosec x + c
= – 3 cot x – 4 cosec x + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
