Calculus - integration

1357

Manish Shankar ·2012-06-17 00:41:56

a+bx=t

1

âˆ«(xdx)/((x^2-a^2)(x^2-b^2))

21

Let x² = z
2x.dx = dz
x.dx = dz/2

12âˆ«dz(z-a²)(z-a²)

12(a²-b²)âˆ«(z-b²) - (z-a²)(z-a²)(z-b²)dz

12(a²-b²)âˆ«(1(z-a²) - 1(z-b²))dz

36

alternate way..

given, I = âˆ«x²(a + bx)²

= 1/b² âˆ« (a + bx - a)²(a + bx)²

Now really easy....!!
break the square and proceed furthur...

integration