Advertisements
Advertisements
Question
Integrate the functions:
cot x log sin x
Solution
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
RELATED QUESTIONS
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Evaluate: `int 1/(x(x-1)) dx`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
Evaluate: `int log ("x"^2 + "x")` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int cos^7 x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).