Advertisements
Advertisements
प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
उत्तर
Let `I=int (1+logx)/(x(2+logx)(3+logx))dx`
Put
`logx=t`
`1/xdx=dt`
`I=int(1+t)/((2+t)(3+t))dt`
consider
`(1+t)/((2+t)(3+t))=A/(2+t)+B/(3+t)`
`(1+t)=A(3+t)+B(2+t)`
A=-1,B=2
`(1+t)/((2+t)(3+t))=-1/(2+t)+2/(3+t)`
`I=int-1/(2+t)dt+int2/(3+t)dt`
`=-log|(2+t)|+2log|(3+t)|+c`
`=log[|((3+t)^2)/(2+t)|] +c`
`=log[|(3+logx)^2/(2+logx)|]+C`
APPEARS IN
संबंधित प्रश्न
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
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 :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
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)`
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
