Advertisements
Advertisements
प्रश्न
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
विकल्प
sin 2x + c
cos 2x + c
tan 2x + c
2 sin 2x + c
उत्तर
sin 2x + c
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Solve: dy/dx = cos(x + y)
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int 1/(cos x - sin x)` dx = _______________
`int cos sqrtx` dx = _____________
`int (log x)/(log ex)^2` dx = _________
`int sqrt(1 + sin2x) "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int (logx)^2/x dx` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int sin^2(x/2)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
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`
Evaluate `int (1 + x + x^2/(2!)) dx`
