Advertisements
Advertisements
Question
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Options
10x - x10 + C
10x + x10 + C
(10x - x10)-1 + C
log (10x + x10) + C
Advertisements
Solution
log (10x + x10) + C
Explanation:
Let `I = int (10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx`
Put x10 + 10x = t
(10x9 + 10x loge 10) dx = dt
`therefore I = int dt/d`
= log |t| + C
= log (10x + x10) + C
APPEARS IN
RELATED QUESTIONS
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`xsqrt(x + 2)`
Write a value of
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
`int sqrt(1 + "x"^2) "dx"` =
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int 1/(cos x - sin x)` dx = _______________
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int cos sqrtx` dx = _____________
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int 1/(sinx.cos^2x)dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
