Advertisements
Advertisements
प्रश्न
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
Advertisements
उत्तर
Let I = `int"e"^x (1/x - 1/x^2) "d"x`
Put f(x) = `1/x`
∴ f'(x) = `-1/x^2`
∴ I = `int"e"^x ["f"(x) + "f'"(x)] "d"x`
= `"e"^x*"f"(x) + "c"`
∴ I = `"e"^x* 1/x + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`1/(1 - tan x)`
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int 1/(sqrt("x") + "x")` dx
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1)) dx`
