Advertisements
Advertisements
प्रश्न
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Advertisements
उत्तर
Let `I = (x + 2)/sqrt(x^2 - 1) dx`
`= int x/sqrt(x^2 - 1) dx + int 2/sqrt(x^2 - 1) dx`
`= I_1 + I_2 + C` (Say) ....(i)
Now `I_1 = int x/sqrt(x^2 - 1) dx`
Put x2 - 1 = t
2x dx = dt
`= 1/2 int dt/sqrtt = 1/2 int t^(-1/2) dt`
`= 1/2 xx t^(1/2)/(1/2) + C_1`
`= sqrtt + C_1 = sqrt (x^2 - 1) + C_1` ....(ii)
and `I_2 = int 2/sqrt(x^2 - 1) dx`
`= 2 log abs (x + sqrt(x^2 - 1) + C_2` .....(iii)
From (i), (ii) and (iii), we get,
`therefore I = sqrt(x^2 - 1) + 2 log abs (x + sqrt(x^2 - 1)) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Find `int dx/(5 - 8x - x^2)`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
What is a standard integral?
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
