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
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Evaluate: `int 1/(x(x-1)) dx`
Solve:
dy/dx = cos(x + y)
Write a value of
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x/(x + 2) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int x^3"e"^(x^2) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
