Advertisements
Advertisements
प्रश्न
Integrate the function in x sin x.
Advertisements
उत्तर
Let `I = int x sin x dx`
`= x int sin x dx - int [d/dx (x) int sin x dx] dx`
[Integration by Parts]
`= x (- cos x) - int 1 (- cos x) dx`
`= - x cos x + int cos x dx`
`= - x cos x + sin x + C`
APPEARS IN
संबंधित प्रश्न
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x sec2 x.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate the following.
`int x^2 e^4x`dx
Evaluate: `int "dx"/("9x"^2 - 25)`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 2) dx = ?
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int_0^1 x tan^-1 x dx` = ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate the following.
`int x^3 e^(x^2) dx`
`inte^(xloga).e^x dx` is ______
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
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`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
