Advertisements
Advertisements
प्रश्न
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Advertisements
उत्तर
To find the value of `int ((1 + log x))/x dx` the proper substitution is 1 + log x = t.
Explanation:
Given integral is `int ((1 + log x) )/x dx`
Let t = 1 + log x
Differentiate w.r.t. x we get,
`dt/dx = 1/x`
⇒ dx = x dt
Now substitute into the integral:
`int t/x dx`
= `int t/x * x dt`
= `∫ t dt`
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`1/(1 - tan x)`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int sec^6 x tan x "d"x` = ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
