Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Advertisements
उत्तर
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
संबंधित प्रश्न
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x log 2x.
Integrate the function in x2 log x.
Integrate the function in e2x sin x.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate:
∫ (log x)2 dx
`int 1/(4x + 5x^(-11)) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int sqrt(tanx) + sqrt(cotx) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
Solve: `int sqrt(4x^2 + 5)dx`
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`int(1-x)^-2 dx` = ______
`int1/(x+sqrt(x)) dx` = ______
Evaluate:
`int (logx)^2 dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
`∫ sin^(−1)` xdx is equal to ______.
Which expression is the integration-by-parts form for a product \(f(x)g(x)\)?
Evaluate \[\int x\cos x\,dx.\]
Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?
