Advertisements
Advertisements
प्रश्न
Evaluate: `int "dx"/("9x"^2 - 25)`
उत्तर
Let I = `int "dx"/("9x"^2 - 25)`
`= int 1/(9 ("x"^2 - 25/9))` dx
`= 1/9 int 1/("x"^2 - (5/3)^2)` dx
`= 1/9 * 1/(2 * 5/3) log |("x" - 5/3)/("x" + 5/3)|` + c
∴ I = `1/30 log |(3"x" - 5)/("3x" + 5)|` + c
APPEARS IN
संबंधित प्रश्न
Integrate the function in tan-1 x.
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
∫ x log x dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int cot "x".log [log (sin "x")] "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.
`int1/sqrt(x^2 - a^2) dx` = ______
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
