Advertisements
Advertisements
Question
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Advertisements
Solution
I = `int (1)/(25 - 9x^2)*dx`
= `int(1)/(5^2 - (3x)^2)*dx`
= `(1)/(2(5))log |(5 + 3x)/(5 - 3x)|*(1)/(3) + c`
= `(1)/(30)log |(5 + 3x)/(5 - 3x)| + c`
Alternative Method:
`int (1)/(25 - 9x^2)*dx`
= `(1)/(9) int (1)/((25)/(9)x^2)*dx`
= `(1)/(9) int (1)/((5/3)^2 - x^2)*dx`
= `(1)/(9) xx (1)/(2 xx 5/3)log|(5/3 + x)/(5 / 3 - x)|+ c`
= `(1)/(30)log|(5 + 3x)/(5 - 3x)| + c`
RELATED QUESTIONS
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sqrt(1 + sin2x) dx`
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int x^x (1 + logx) "d"x`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int ("d"x)/(x(x^4 + 1))` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate `int1/(x(x - 1))dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int1/(x(x - 1))dx`
