Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
पर्याय
tan x – x + c
x + tan x + c
x – tan x + c
– x – cot x + c
Advertisements
उत्तर
x – tan x + c
[ Hint : `int (cos2x - 1)/(cos2x + 1)*dx`
= `int (-(1 - cos2x))/(1 + cos^2x)*dx`
= `int (-2sin^2x)/(2cos^2x)*dx`
= `int (sec^2x - 1)*dx`
= – tan x + x + c.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`(1+ log x)^2/x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int sqrt(1 + sin2x) dx`
`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 sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int(log(logx) + 1/(logx)^2)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)
`int "cosec"^4x dx` = ______.
Evaluate the following.
`intxsqrt(1+x^2)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?
How should a substitution be chosen?
