Advertisements
Advertisements
प्रश्न
Evaluate the following integrals:
`int x/(x + 2).dx`
Advertisements
उत्तर
`int x/(x + 2).dx`
= `int((x + 2) - 2)/(x + 2).dx`
= `int ((x + 2)/(x + 2) - 2/(x + 2)).dx`
= `int 1 dx - 2 int 1/(x + 2).dx`
= x – 2 log |x + 2| + c.
APPEARS IN
संबंधित प्रश्न
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
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 : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int (5"x" + 1)^(4/9)` dx
`int 1/(cos x - sin x)` dx = _______________
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int1/(x(x - 1))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int 1/(x(x-1))dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`intxsqrt(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 the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int 1/(x(x-1)) dx`
