Advertisements
Advertisements
प्रश्न
`int (log x)/(log ex)^2` dx = _________
विकल्प
x (1 + log x) + c
`x/(1 + log x) + "c"`
`1/(1 + log x) + "c"`
`1/(1 - log x) + "c"`
Advertisements
उत्तर
`x/(1 + log x) + "c"`
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
tan2(2x – 3)
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` 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`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
Evaluate `int(3x^2 - 5)^2 "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int dx/(1 + e^-x)` = ______
`int1/(4 + 3cos^2x)dx` = ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sin^2(x/2)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
