Advertisements
Advertisements
Question
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Advertisements
Solution
Let `I = int 1/(cos^2 x . (1 - tan x)^2)` dx
or `= int (sec^2)/(1 - tan)^2` dx `(because 1/(cos^2 x) = sec^2 x)`
1 - tan x = t
- sec2 x dx = dt
∴ `I = - int dt/t^2 = (t^(-2+1))/(-2 + 1) + C`
`= 1/t + C = 1/ (1 - tanx) + C`
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
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 : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int sqrt(1 + sin2x) dx`
`int sin^-1 x`dx = ?
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int cos^3x dx` = ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int 1/("x"("x" - 1)) "dx"`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int "cosec"^4x dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
