Advertisements
Advertisements
Question
Integrate the functions:
cot x log sin x
Advertisements
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:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Write a value of
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log 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 : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate `int 1/(x (x - 1))` dx
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/("x" log "x")`dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
`int cot^2x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
Evaluate `int(3x^2 - 5)^2 "d"x`
`int sec^6 x tan x "d"x` = ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int x^3 e^(x^2) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int sin^2(x/2)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Integration by substitution is the reverse process of which rule?
