Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Advertisements
उत्तर
`int tanx/(sec x + tan x)dx`
= `int tanx/(sec x + tan x) xx (secx - tanx)/(sec - tan x)dx`
= `int(sec x tan x - tan^2x)/(sec^2x - tan^2x)dx`
= `int(se c tan x - (sec^2x - 1))/(1)dx`
= `int sec x tan x dx - int sec^2 x dx + int 1 dx`
= sec x – tan x + x + c.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`1/(1 - tan x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int a^x e^x \text{ dx }\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int cos^2x.dx`
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^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int cos sqrtx` dx = _____________
Evaluate `int(3x^2 - 5)^2 "d"x`
`int x^3"e"^(x^2) "d"x`
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate `int1/(x(x - 1))dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
