Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Advertisements
उत्तर
I = `int sin^-1 ((2x)/(1 + x^2)) ""d"x`
Put x = tan θ
dx = sec2θ dθ
I = `int sin^-1 ((2tantheta)/(1 + tan^2theta)) sec^2theta "d"theta`
= `int sin^-1 (sin2theta) sec^2theta "d"theta`
= `int 2theta sec^2theta "d"theta`
= `2int (theta) (sec^2theta "d"theta)` ........[Rater Example 11.34]
I = `2[thetatantheta - int tan theta "d"theta]`
= `2theta tan theta - 2 log |sectheta| + "c"` ......`(sec theta = sqrt(1 + tan^2theta))`
`int sin^-1 ((2x)/(1 + x^2)) "d"x = 2x tan^-1x - 2log |sqrt(1 + x^2)| + "c"`
= `2[x tan^-1x - log |sqrt(1 + x^2)|] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "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
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
