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`
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Choose the correct alternative:
`int secx/sqrt(cos2x) "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 ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
