Advertisements
Advertisements
Question
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Options
`(3)^("x"^3) + "c"`
`(3)^("x"^3)/(3 * log 3) + "c"`
`log 3 (3)^("x"^3)` + c
`"x"^2 (3)^("x"^3) + "c"`
Solution
`(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
RELATED QUESTIONS
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int log ("x"^2 + "x")` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int cot^2x "d"x`
`int cos^7 x "d"x`
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`int1/(x^2+4x-5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
