Advertisements
Advertisements
प्रश्न
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
पर्याय
`(3)^("x"^3) + "c"`
`(3)^("x"^3)/(3 * log 3) + "c"`
`log 3 (3)^("x"^3)` + c
`"x"^2 (3)^("x"^3) + "c"`
Advertisements
उत्तर
`(3)^("x"^3)/(3 * log 3) + "c"`
Explanation:
Let I = `int "x"^2 * (3)^("x"^3) "dx"`
Put x3 = t
∴ `3"x"^2 "dx" = "dt"`
∴ `"x"^2 "dx" = 1/3 "dt"`
∴ I = `1/3 int 3^"t" * "dt"`
`= 1/3 * 3^"t"/log 3` + c
`= (3)^("x"^3)/(3 log 3)` + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int1/(x(x - 1))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?
