Advertisements
Advertisements
प्रश्न
`int "dx"/(("x" - 8)("x" + 7))`=
विकल्प
`1/15 log |("x" + 2)/("x" - 1)| + "c"`
`1/15 log |("x" + 8)/("x" + 7)| + "c"`
`1/15 log |("x"- 8)/("x" + 7)| + "c"`
(x − 8)(x − 7) + c
`1/15 log |("x" + 2)/("x"+ 1)| + "c"`
(x − 8)(x + 7) + c
उत्तर
`bb(1/15 log |("x"- 8)/("x" + 7)| + "c")`
Explanation:
I = `int "A"/("x" - 8) + "B"/("x" + 7)"dx"`
1 = A(x + 7) + B(x − 8)
When x = 8, A = `1/15` and x = −7, B = `(-1)/15`
∴ I = `int 1/15 (1/("x" - 8)) "dx" + int (-1)/15 (1/("x "+ 7)) "dx"`
= `int 1/15 log ("x" - 8)"dx" - int 1/15 log ("x" + 7)`
= `int 1/15 {log (("x" - 8)/("x" + 7))} + "c"`
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Find : `int x^2/(x^4+x^2-2) dx`
Evaluate: `∫8/((x+2)(x^2+4))dx`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t. x : `(1)/(sinx*(3 + 2cosx)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx
Evaluate: `int 1/("x"("x"^5 + 1))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
`int (2x - 7)/sqrt(4x- 1) dx`
`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int sec^3x "d"x`
`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int 1/(sinx(3 + 2cosx)) "d"x`
`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5) "d"x`
If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
Evaluate the following:
`int (x^2"d"x)/(x^4 - x^2 - 12)`
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.
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
