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
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int 1/(xsin^2(logx)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
