Advertisements
Advertisements
Question
Evaluate the following integrals : `int sin x/cos^2x dx`
Advertisements
Solution
`int sin x/cos^2x dx = int(1/cosx)(sinx/cosx)dx`
= `intsec x tan x dx`
= sec x + c.
APPEARS IN
RELATED QUESTIONS
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
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 "e"^sqrt"x"` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int(log(logx))/x "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int (f^'(x))/(f(x))dx` = ______ + c.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
