Advertisements
Advertisements
प्रश्न
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Advertisements
उत्तर
\[\int \sqrt{x^2 - 9} \text{ dx }\]
\[ = \int \sqrt{x^2 - 3^2} \text{ dx}\]
\[ = \frac{x}{2}\sqrt{x^2 - 3^2} - \frac{3^2}{2}\text{ ln} \left| x + \sqrt{x^2 - 3} \right| + C \left( \because \sqrt{x^2 - a^2} = \frac{x}{2}\sqrt{x^2 - a^2} - \frac{a^2}{2}\text{ ln } \left| x + \sqrt{x^2 + a^2} \right| + C \right)\]
\[ = \frac{x}{2}\sqrt{x^2 - 9} - \frac{9}{2}\text{ ln } \left| x + \sqrt{x^2 - 9} \right| + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
`int cos sqrtx` dx = _____________
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1)) dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
