Advertisements
Advertisements
प्रश्न
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
Advertisements
उत्तर
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x = int "e"^x[(x + 4 - 1)/(x + 4)^2] "d"x`
= `int "e"^x[1/(x + 4) - 1/(x + 4)^2] "d"x`
= `"e"^x(1/(x + 4)) + "c"` .......`[∵ int"e"^x["f"(x) + "f'"(x)] "d"x = "e"^x*"f"(x) + "c"]`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
cot x log sin x
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int sqrt(1 + "x"^2) "dx"` =
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (sin4x)/(cos 2x) "d"x`
`int x/(x + 2) "d"x`
`int(log(logx))/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (cos x)/(1 - sin x) "dx" =` ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
`int 1/(sinx.cos^2x)dx` = ______.
Write `int cotx dx`.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
