Advertisements
Advertisements
प्रश्न
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Advertisements
उत्तर
`int x/((x + 2)(x + 3)) dx = bb(int (-2)/(x + 2))dx + int 3/(x + 3) dx`
Explanation:
Let `x/((x + 2)(x + 3)) = A/(x + 2) + B/(x + 3)`
⇒ x = A(x + 3) + B(x + 2)
⇒ x = (A + B)x + (3A + 2B)
On equating coefficients of like terms, we get
A + B = 1 .......(1)
⇒ B = 1 – A
⇒ B = 1 – (– 2) = 3
⇒ B = 3
And 3A + 2B = 0 ......(2)
⇒ 3A + 2(1 – A) = 0
⇒ 3A + 2 – 2A = 0
⇒ A + 2 = 0
⇒ A = – 2
∴ `int x/((x + 2)(x + 3)) dx = int (-2)/(x + 2) dx + int 3/(x + 3) dx`
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
Integrate the function in x sin−1 x.
Integrate the function in x tan-1 x.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int 1/(4x + 5x^(-11)) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Solve: `int sqrt(4x^2 + 5)dx`
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following:
`intx^3e^(x^2)dx`
The value of `inta^x.e^x dx` equals
