Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Advertisements
उत्तर
Let `I = int x^2/(2 + 3x^3)^3` dx
Put 2 + 3x3 = t
9x2 dx = dt
or x2 dx `= 1/9` dt
∴ `I = 1/9 int dt/t^3 = 1/9 int t^-3 dt`
`= 1/9 t^-2/(-2) + C = -1/18 t^-2 + C`
`= -1/ (18(2 + 3x^3)^2) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
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 : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int sin^3x cos^3x 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`
Evaluate `int (1 + x + x^2/(2!)) dx`
