Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Advertisements
उत्तर
`int(2x^3 - 5x + 3/x + 4/x^5)dx`
= `2intx^3 dx - 5 int x dx + 3 int1/x dx + 4 int x^-5 dx`
= `2(x^4/4) - 5(x^2/2) + 3 log |x| + 4(x^-4/(-4)) + c`
= `x^4/(2) - (5)/(2) x^2 + 3 log |x| - (1)/x^4 + c`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(1+ log x)^2/x`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of
Write a value of
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int x^2/sqrt(1 - x^6)` dx = ________________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Evaluate `int (1)/(x(x - 1))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
What is the value of \[\int\sin^3x\cos^2x\,dx\]?
