Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Advertisements
Solution
`int (sin^2x)/(1 + cosx) "d"x = int (1 - cos^2x)/(1 + cosx) "d"x`
= `int ((1 + cosx) xx (1 - cosx))/(1 + cosx) "d"x`
= `int (1 - cosx) "d"x`
= `int "d"x - int cosx "d"x`
= x – sin x + c
APPEARS IN
RELATED QUESTIONS
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 :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
