Advertisements
Advertisements
Question
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Advertisements
Solution
`int (cos2x)/sin^2x dx`
= `int((1 - 2sin^2x))/sin^2x dx`
= `int(1/sin^2x - (2sin^2x)/sin^2x)dx`
= `int "cosec"^2x dx - 2 int dx`
= – cot x – 2x + c.
APPEARS IN
RELATED QUESTIONS
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
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 : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (sin4x)/(cos 2x) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int cot^2x "d"x`
`int cos^7 x "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int cos^3x dx` = ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sin^2(x/2)dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int 1/(x(x-1)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
