Advertisements
Advertisements
प्रश्न
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Advertisements
उत्तर
Let `I = ((x - 3) e^x)/(x - 1)^3 dx`
`= int (e^x (x - 1 - 2))/(x - 1)^3 dx`
`= int e^x [1/((x - 1)^2) - 2/((x - 1)^3)] dx`
On substituting `e^x . 1/((x - 1)^2) = t`
`[e^x - 2 (x - 1)^-3 + 1/((x - 1)^2). e^x] dx = dt`
or `e^x [1/((x - 1)^2) - 2/(x - 1)^3] dx = dt`
Hence, `I = int 1. dt = t + C`
`= e^x/((x - 1)^2) + C`
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
Integrate the function in `x^2e^x`.
Integrate the function in x log x.
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
Evaluate:
∫ (log x)2 dx
`int ("d"x)/(x - x^2)` = ______
`int(x + 1/x)^3 dx` = ______.
`int 1/x "d"x` = ______ + c
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
`int 1/sqrt(x^2 - a^2)dx` = ______.
Evaluate:
`intcos^-1(sqrt(x))dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate the following.
`intx^3 e^(x^2)dx`
Which pair is listed as Trigonometric in the LIATE rule?
For \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx,\] which functions are chosen as the first function and the second function?
