Advertisements
Advertisements
प्रश्न
Evaluate:
`int (x + 7)/(x^2 + 4x + 7)dx`
उत्तर
Let I = `int (x + 7)/(x^2 + 4x + 7)dx`
On applying partial integration method
`x + 7 = "A" d/dx(x^2 + 4x + 7) + "B"`
x + 7 = A(2x + 4) + B
Then, A = `1/2` and B = 5
Then, I = `int(1/2(2x + 4) + 5)/(x^2 + 4x + 7)dx`
= `1/2 int ((2x + 4))/(x^2 + 4x + 7)dx + 5 int 1/((x^2 + 4x + 7))dx`
= `1/2 log |x^2 + 4x + 7| + 5 int 1/((x + 2)^2 + (sqrt(3))^2) dx + c`
= `1/2 log |x^2 + 4x + 7| + 5/sqrt(3) tan^-1((x + 2)/sqrt(3)) + c`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`
Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx
`int (2x - 7)/sqrt(4x- 1) dx`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
Evaluate:
`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5) "dt"`
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.
Evaluate: `int (dx)/(2 + cos x - sin x)`
If f(x) = `int(3x - 1)x(x + 1)(18x^11 + 15x^10 - 10x^9)^(1/6)dx`, where f(0) = 0, is in the form of `((18x^α + 15x^β - 10x^γ)^δ)/θ`, then (3α + 4β + 5γ + 6δ + 7θ) is ______. (Where δ is a rational number in its simplest form)
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Evaluate:
`int 2/((1 - x)(1 + x^2))dx`
Evaluate.
`int (5x^2 - 6x + 3) / (2x -3) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
