Advertisements
Advertisements
प्रश्न
Integrate the functions:
cot x log sin x
Advertisements
उत्तर
Let `I = int cot x log sin x dx`
Put log sin x = t
`1/sinx` . cos x dx = dt
`I = int t dt`
or cot x dx = dt
∴ `I = int t dt = t^2/2 + C`
`= 1/2 [log (sin x)]^2 + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
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:
`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 : `sin(x - a)/cos(x + b)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate `int 1/((2"x" + 3))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int (sin4x)/(cos 2x) "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?
How should a substitution be chosen?
