Advertisements
Advertisements
Question
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Solution
Let I = `int 1/(2"x" + 3"x" * log"x")` dx
`= int 1/("x"(2 + 3 log "x"))` dx
Put 2 + 3 log x = t
∴ `3 * 1/"x" "dx"` = dt
∴ `1/"x" "dx" = 1/3 "dt"`
∴ I = `1/3 int 1/"t" * "dt"`
`= 1/3` log |t| + c
∴ I = `1/3` log |2 + 3 log x| + c
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals : `int(4x + 3)/(2x + 1).dx`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int cos sqrtx` dx = _____________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int (cos2x)/(sin^2x) "d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
