Advertisements
Advertisements
Question
Find the integrals of the following:
`1/(25 - 4x^2)`
Advertisements
Solution
`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
RELATED QUESTIONS
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.
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 :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
