Advertisements
Advertisements
Question
`int sqrt(1 + sin2x) "d"x`
Solution
`int sqrt(1 + sin2x) "d"x = int sqrt(sin^2x + cos^2x + 2sinx cosx) "d"x`
= `int sqrt((cosx + sinx)^2) "d"x`
= `int (cosx + sinx) "d"x`
= sin x – cos x + c
APPEARS IN
RELATED QUESTIONS
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`(10x^9 10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Integrate the following w.r.t.x : `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int sqrt(1 + "x"^2) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int sin^-1 x`dx = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
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 ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int cos^3x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) 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`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
`int "cosec"^4x dx` = ______.
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`