Advertisements
Advertisements
प्रश्न
Integrate the function in x sin 3x.
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x log x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following : `int(sin(logx)^2)/x.log.x.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 : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : log (x2 + 1)
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
`intsqrt(1+x) dx` = ______
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))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 `int tan^-1x dx`
Evaluate the following:
`intx^3e^(x^2)dx`
