Advertisements
Advertisements
Question
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Solution
`int(5x + 2)/(3x - 4).dx`
= `int(5/3 (3x - 4) + 20/3 + 2)/(3x - 4) dx`
= `int(5/3 (3x - 4) + 26/3)/(3x - 4) dx`
= `int[5/3 + ((26/3))/(3x - 4)] dx`
= `(5)/(3)int 1 dx + (26)/(3) int 1/(3x - 4) dx`
= `(5)/(3)x + (26)/(3).(1)/(3)log|3x - 4| + c`
= `(5)/(3)x + (26)/(9)log|3x - 4| + c`
APPEARS IN
RELATED QUESTIONS
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`(1+ log x)^2/x`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals : `int cos^2x.dx`
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 : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (cos2x)/(sin^2x) "d"x`
`int x/(x + 2) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
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)`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Write `int cotx dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int x^3 e^(x^2) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
