Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
पर्याय
sin 2x + c
cos 2x + c
tan 2x + c
2 sin 2x + c
Advertisements
उत्तर
sin 2x + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
`int sqrt(1 + "x"^2) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
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`.
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
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"e"^x (1/x - 1/x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
