Advertisements
Advertisements
प्रश्न
Evaluate the following: `int sinx/(sin 3x).dx`
Advertisements
उत्तर
Let I = `int sinx/(sin 3x).dx`
= `int sinx/(3sinx - 4sin^3x).dx`
= `int (sinx)/(sinx(3 - 4sin^2x)).dx`
= `int (1)/(3 - 4sin^2x).dx`
Dividing both numerator and denominator by cos2x, we get
I = `int (sec^2x)/(3sec^2x - 4tan^2x).dx`
= `int (sec^2x)/(3(1 + tan^2x) - 4tan^2x).dx`
= `int (sec^2x)/(3 - tan^2x).dx`
Put tan x = t
∴ sec2x dx = dt
I = `int dt/(3-t^2)`
I = `int dt/((sqrt(3))^2 - t^2)`
= `int1/((sqrt3)^2 - t^2)dt`
= `(1)/(2sqrt(3)) log |(sqrt(3) + t)/(sqrt(3) - t)| + c`
= `(1)/(2sqrt(3)) log |(sqrt(3) + tanx)/(sqrt(3) - tanx)| + c`.
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(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:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "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 = ?
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int cos sqrtx` dx = _____________
`int 1/(xsin^2(logx)) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
