Advertisements
Advertisements
प्रश्न
Find: `int sin^-1 (2x) dx.`
Advertisements
उत्तर
`int sin^-1 (2x) dx`
Using ILATE rule
`x sin^-1 2x - int (2x)/sqrt(1-4x^2)dx`
`x sin^-1 2x + 1/4 int (-8x)/sqrt(1-4x^2) dx`
Taking 1 - 4x2 = t
⇒ - 8x dx = dt
`x sin^-1 2x + 1/4 int dt/sqrt(t)`
`x sin^-1 2x + 1/4 (2t 1/2)/1 + "C"`
= `x sin^-1 2x + (t 1/2)/2 + "C"`
= `x sin^-1 2x + sqrt(1-4x^2)/2 + "C"`
APPEARS IN
संबंधित प्रश्न
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
sin4 x
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
tan3 2x sec 2x
Find the integrals of the function:
`(cos 2x+ 2sin^2x)/(cos^2 x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
sin−1 (cos x)
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ (log "x")^2 d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find `int "dx"/(2sin^2x + 5cos^2x)`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int sqrt(1 + sinx)"d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
