Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Advertisements
उत्तर
`int ("d"x)/sqrt(x^2 + 4x + 2) = int ("d"x)/sqrt((x + 2)^2 - 2^2 + 2)`
= `int ("d"x)/sqrt((x + 2)^2 - 4 + 2)`
= `int ("d"x)/sqrt((x + 2)^2 - 2)`
= `int ("d"x)/sqrt((x + 2)^2 - (sqrt(2))^2`
Put x + 2 = t
dx = dt
= `int ("d"x)/sqrt("t"^2 - (sqrt(2))^2`
`int ("d"x)/sqrt(x^2 - "a"^2) = log|x + sqrt(x^2 - "a"^2)| + "c"`
= `log |"t" + sqrt("t"^2 - (sqrt(2))^2)| + "c"`
= `log |(x + 2) + sqrt((x + 2)^2 - 2)| + "c"`
= `log |(x + 2) + sqrt(x^2 + 4x + 4 - 2)| + "c"`
`int ("d"x)/sqrt(x^2 + 4x + 2) = log|(x + 2) + sqrt(x^2 + 4x + 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.
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
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 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
