Advertisements
Advertisements
Question
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Advertisements
Solution
Let I = `int (1)/(xsin^2(logx))*dx`
Put log x = t
∴ `(1)/x*dx` = dt
∴ I = `int (1)/sin^2t*dt`
= `int "cosec"^2tdt`
= – cot t + c
= – cot (log x) + c.
APPEARS IN
RELATED QUESTIONS
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x log 2x.
Integrate the function in x sec2 x.
Integrate the function in tan-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Find :
`∫(log x)^2 dx`
Evaluate the following : `int x.cos^3x.dx`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : e2x sin x cos x
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate:
∫ (log x)2 dx
`int (sinx)/(1 + sin x) "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int(x + 1/x)^3 dx` = ______.
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
∫ log x · (log x + 2) dx = ?
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
`int_0^1 x tan^-1 x dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Solution of the equation `xdy/dx=y log y` is ______
`int logx dx = x(1+logx)+c`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`int (logx)^2 dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Which function is an example under priority \(I\) in the LIATE rule?
Evaluate \[\int x\cos x\,dx.\]
