Advertisements
Advertisements
Question
`int(x + 1/x)^3 dx` = ______.
Options
`1/4(x + 1/x)^4 + c`
`x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c`
`x^4/4 + (3x^2)/2 + 3log x + 1/x^2 + c`
`(x - x^(-1))^3 + c`
Solution
`int(x + 1/x)^3 dx` = `bb(underline(x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c))`.
Explanation:
`(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3`
∴ `int(x + 1/x)^3dx = int(x^3 + 3x + 3/x + 1/x^3)dx`
= `x^4/4 + (3x^2)/2 + 3logx - 1/(2x^2) + c`
APPEARS IN
RELATED QUESTIONS
Integrate : sec3 x w. r. t. x.
Integrate the function in x log 2x.
Integrate the function in x sec2 x.
Integrate the function in (x2 + 1) log x.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
`int 1/(4x + 5x^(-11)) "d"x`
`int sin4x cos3x "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int logx/(1 + logx)^2 "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Solution of the equation `xdy/dx=y log y` is ______
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Evaluate:
`int (logx)^2 dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
