Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/(25 - 4x^2)`
उत्तर
`int 1/(25 - 4x^2) "d"x = int 1/(4(25/4 - x^2)) "d"x`
= `1/4 int ("d"x)/((5/4)^2 - x^2)`
`int ("d"x)/("a"^2 - x^2) = 1/(2"a") log |("a" + x)/("a" - x)| + "c"`
= `1/4 xx 1/(2 xx (5/2)) log |(5/2 + x)/(5/2 - x)| + "c"`
= `1/4 xx 1/5 log |((5 + 2x)/2)/((5 - 2x)/2)| + "c"`
= `1/20 log |(5 + 2x)/(5 - 2x)| + "c"`
APPEARS IN
संबंधित प्रश्न
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:\
`logx/(1 + log)^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:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
