Advertisements
Advertisements
प्रश्न
`int 1/sqrt(x^2 - a^2)dx` = ______.
Advertisements
उत्तर
`int 1/sqrt(x^2 - a^2)dx` = `bb(underline(log|x + sqrt(x^2 - a^2)| + c)`.
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
Integrate the function in x2 log x.
Integrate the function in x tan-1 x.
Integrate the function in x (log x)2.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int 1/sqrt(2x^2 - 5) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int logx/(1 + logx)^2 "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`intsqrt(1+x) dx` = ______
Solution of the equation `xdy/dx=y log y` is ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
Evaluate:
`int (logx)^2 dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x^3 e^(x^2) dx`
The value of `inta^x.e^x dx` equals
