Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(logx)^n/x`
Advertisements
उत्तर
Let I = `int (logx)^n/x.dx`
Put log x = t.
∴ `(1)/x.dx = dt`
∴ I = `int t^n dt`
= `(t^(n + 1))/(n + 1) + c`
= `(1)/(n + 1).(logx)^(n + 1) + c`.
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate `int (3"x"^2 - 5)^2` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
`int "cosec"^4x dx` = ______.
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(1+x+x^2/(2!))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
