Advertisements
Advertisements
प्रश्न
`int "dx"/(("x" - 8)("x" + 7))`=
पर्याय
`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`
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`x/((x -1)^2 (x+ 2))`
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 : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Evaluate: `int "x"/(("x - 1")^2("x + 2"))` dx
State whether the following statement is True or False.
If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int (2x - 7)/sqrt(4x- 1) dx`
`int x^2sqrt("a"^2 - x^6) "d"x`
`int sqrt(4^x(4^x + 4)) "d"x`
`int (sinx)/(sin3x) "d"x`
`int x sin2x cos5x "d"x`
Evaluate:
`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`
`int xcos^3x "d"x`
Evaluate `int x^2"e"^(4x) "d"x`
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
