Advertisements
Advertisements
Question
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Advertisements
Solution
`int (cos2x)/(sin^2x.cos^2x)dx`
= `int(cos^2x - sin^2x)/(sin^2x.cos^2x)dx`
= `int(1/sin^2x - 1/cos^2x)dx`
= `int "cosec"^2x dx - int sec^2 x dx`
= – cot x – tan x + c.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: ∫ |x| dx if x < 0
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int sin^-1 x`dx = ?
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
