Advertisements
Advertisements
Question
Integrate the function in x sin 3x.
Advertisements
Solution
Let `I = int x. sin 3x dx`
`= x int sin 3x dx - int [d/dx x int sin 3x dx] dx`
`= x (- (cos 3x)/3) - int 1 ((- cos 3x)/3) dx`
`= (x cos 3x)/3 + 1/3 int cos 3x dx`
`= (x cos 3x)/3 + 1/3* (sin 3x)/3 + C`
`= - (x cos 3x)/3 + 1/9 sin 3x + C`
APPEARS IN
RELATED QUESTIONS
Integrate the function in tan-1 x.
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int sqrt(tanx) + sqrt(cotx) "d"x`
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`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
`int(logx)^2dx` equals ______.
`int_0^1 x tan^-1 x dx` = ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int x^2 cos x dx`
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
`∫ sin^(−1)` xdx is equal to ______.
Which pair is listed as Exponential in the LIATE rule?
Repeated parts may be needed for which pair of integrals?
