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: `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 - tan x)`
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
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of
Write a value of
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/(cos x - sin x)` dx = _______________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int1/(x(x - 1))dx`
