Advertisements
Advertisements
प्रश्न
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
उत्तर
\[\int \sqrt{9 + x^2} \text{ dx }\]
\[ = \int \sqrt{3^2 + x^2} dx \left( \because \sqrt{a^2 + x^2} = \frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\text{ ln }\left| x + \sqrt{x^2 + a^2} \right| \right)\]
\[ = \frac{x}{2}\sqrt{9 + x^2} + \frac{9}{2}\text{ ln }\left| x + \sqrt{9 + x^2} \right| + C\]
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
sec2(7 – 4x)
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sinx/(sin 3x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int cot^2x "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sin^2(x/2)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int1/(x(x - 1))dx`
