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
Advertisements
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
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`
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 "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int sqrt(4^x(4^x + 4)) "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`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 (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
`int x/((x - 1)^2 (x + 2)) "d"x`
If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Let g : (0, ∞) `rightarrow` R be a differentiable function such that `int((x(cosx - sinx))/(e^x + 1) + (g(x)(e^x + 1 - xe^x))/(e^x + 1)^2)dx = (xg(x))/(e^x + 1) + c`, for all x > 0, where c is an arbitrary constant. Then ______.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
When is a rational function called improper?
What should be checked before beginning partial-fraction decomposition?
What must be included for a repeated linear factor?
