Advertisements
Advertisements
प्रश्न
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Advertisements
उत्तर
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + 4 log|x-1| + c
संबंधित प्रश्न
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate:
∫ (log x)2 dx
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int 1/x "d"x` = ______ + c
`int"e"^(4x - 3) "d"x` = ______ + c
`int log x * [log ("e"x)]^-2` dx = ?
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?
Which pair is listed as Exponential 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?
For the special integral \[\int e^x\left[f(x)+f'(x)\right]dx,\] what is the antiderivative?
Which differentiation identity verifies the special integral \[\int e^x\left[f(x)+f'(x)\right]dx=e^xf(x)+C?\]
