Advertisements
Advertisements
Question
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`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 = ?
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int sin^-1 x`dx = ?
`int cos^3x dx` = ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`intsqrt(sec x/2 - 1)dx`
