Advertisements
Advertisements
प्रश्न
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
पर्याय
sin 2x + c
cos 2x + c
tan 2x + c
2 sin 2x + c
Advertisements
उत्तर
sin 2x + c
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(1 + sin2x) dx`
`int cot^2x "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
