Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Advertisements
उत्तर
Let I = `int (sin6x)/(sin 10x sin 4x).dx`
= `int (sin (10x - 4x))/(sin 10x sin 4x).dx`
= `int (sin 10x cos 4x - cos 10x sin 4x)/(sin 10x sin 4x).dx`
= `int [(sin 10x cos 4x)/(sin 10x sin 4x) - (cos 10x sin 4x)/(sin 10x sin 4x)].dx`
= `int cot 4x dx - int cot 10x dx`
= `(1)/(4)log|sin4x| - (1)/(10)log|sin 10x| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int (1 + x)/(x + "e"^(-x)) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int1/(x(x - 1))dx`
