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
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(4 - x^2)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
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 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
