Advertisements
Advertisements
प्रश्न
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Advertisements
उत्तर
Let I = `int (3"x"^3 - 2sqrt"x")/"x"` dx
`= int ("3x"^3/"x" - "2x"^(1/2)/"x")` dx
`= int (3"x"^2 - 2"x"^(-1/2))` dx
`= 3 int "x"^2 * "dx" - 2 int "x"^(-1/2) * "dx"`
`= 3 ("x"^3/3) - 2("x"^(1/2)/(1/2))` + c
∴ I = x3 - 4`sqrt"x"` + c
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate `int 1/(x (x - 1))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
`int cot^2x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int sec^6 x tan x "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
When applying substitution, what must always be rewritten in terms of the new variable?
