Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Advertisements
उत्तर
Let I = `int e^x (1/x - 1/x^2)`dx
Put f(x) = `1/x`
∴ f '(x) = `1/x`
∴ I = `int e^x [f(x) + f '(x)]` dx
`= e^x * f(x) + c`
∴ I = `e^x * 1/x + c`
∴ I = `(e^x)/x + c`
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x sin 3x.
Integrate the function in x log x.
Integrate the function in tan-1 x.
Integrate the function in x (log x)2.
Find :
`∫(log x)^2 dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int(x + 1/x)^3 dx` = ______.
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
∫ log x · (log x + 2) dx = ?
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
Solve: `int sqrt(4x^2 + 5)dx`
`int(logx)^2dx` equals ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
