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
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 x.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int x.cos^3x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
`int 1/sqrt(2x^2 - 5) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
`intsqrt(1+x) dx` = ______
`int1/(x+sqrt(x)) dx` = ______
Solve the following
`int_0^1 e^(x^2) x^3 dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
Which function is an example under priority \(I\) in the LIATE rule?
Evaluate \[\int x\cos x\,dx.\]
Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?
Evaluate \[\int e^x\sin x\,dx.\]
For the special integral \[\int e^x\left[f(x)+f'(x)\right]dx,\] what is the antiderivative?
