Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Advertisements
उत्तर
I = `int (1)/(7 + 2x^2).dx`
= `(1)/(2) int (1)/(7/2 + x^2).dx`
= `(1)/(2) int (1)/((sqrt(7/2))^2 + x^2).dx`
= `(1)/(2).(1)/((sqrt(7/2))) tan^-1 |x/sqrt(7/2)| + c`
= `(1)/sqrt(14)tan^-1 |(sqrt(2)x)/sqrt(7)| + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate `int 1/((2"x" + 3))` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int (cos x)/(1 - sin x) "dx" =` ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int cos^3x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following
`int x^3 e^(x^2) ` 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 the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`intsqrt(sec x/2 - 1)dx`
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
After choosing \[u=g(x)\], what is the next step?
