Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
विकल्प
True
False
Advertisements
उत्तर
True
संबंधित प्रश्न
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (x2 + 1)
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
∫ log x · (log x + 2) dx = ?
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`int(logx)^2dx` equals ______.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int logx dx = x(1+logx)+c`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
