Advertisements
Advertisements
प्रश्न
`int logx/x "d"x`
Advertisements
उत्तर
Put log x = t
∴ `1/x "d"x` = dt
∴ `int logx/x "d"x = int "t" "dt"`
= `"t"^2/2 + "c"`
`((log x)^2)/2 + "c"`
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/(cos x - sin x)` dx = _______________
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int dx/(1 + e^-x)` = ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int (logx)^2/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate `int 1/("x"("x" - 1)) "dx"`
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 (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int 1/(x(x-1)) dx`
