Advertisements
Advertisements
Question
`int ("x" + 1/"x")^3 "dx"` = ______
Options
`1/4 ("x" + 1/"x")^4` + c
`"x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c"`
`"x"^4/4 + "3x"^2/2 + 3 log "x" + 1/"x"^2 + "c"`
`("x" - "x"^-1)^3` + c
Solution
`int ("x" + 1/"x")^3 "dx"` = `bbunderline("x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c")`
Explanation:
Let I = `int ("x" + 1/"x")^3 "dx"`
`int ("x"^3 + "3x" + 3/"x" + 1/"x"^3)` dx
`= "x"^4/4 + 3 "x"^2/2 + 3 log |"x"| - 1/"2x"^2` + c
APPEARS IN
RELATED QUESTIONS
Integrate the function in x sin x.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following : `int x^2.log x.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
`int "e"^x x/(x + 1)^2 "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Find: `int e^x.sin2xdx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`intsqrt(1+x) dx` = ______
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
