Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Advertisements
उत्तर
Let I =`int "e"^x ((x - 1)/2x^2) "d"x`
= `1/2 int "e"^x (x/x^2 - 1/x^2) "d"x`
= `1/2 int "e"^x (1/x - 1/x^2) "d"x`
Take f(x) = `1/x`
f'(x) = `- 1/x^2`
`[int "e"^x ["f"(x) + "f"(x)] "d"x = "e"^x "f"(x) + "c"]`
∴ I = `1/2 "e"^x 1/x + "c"`
I = `"e"^x/(2x) + "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.
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
