| The indefinite integrals
containing quadratic polynomial of the form
|
 |
|
|
We solve given integral by separating
the derivative of the quadratic polynomial in the numerator, thus
|
|
|
| therefore, the solution of I2
depend on the leading coefficient a
and the vertical translation y0,
i.e.,
|
| a
)
if |
 |
then, |
|
|
|
|
| b
)
if |
 |
then, |
|
|
|
|
|
|
|
|
|
| The indefinite integrals
containing quadratic polynomial of the form
|
 |
|
|
|
| The integrand function to be real, the
quadratic polynomial in the denominator must be positive,
therefore
|
| a
) if a
> 0 and
y0
is not
0 then
|
|
|
| b
) if a
< 0 and
y0
>
0 then
|
|
|
|
c
) if a
> 0 and
y0 =
0 then
|
|
|
|
| The indefinite integrals
containing quadratic polynomial of the form
|
 |
|
| Use similar methods to solve this
integral as in the preceding example. Hence,
the solutions depend on the sign of the leading
coefficient
a
and the sign or the value of the vertical translation y0.
|
|
|
|
|
Let solve given integral by separating
the derivative of the quadratic polynomial in the numerator.
|
|
|
|
| The indefinite integrals
containing quadratic polynomial of the form
|
 |
|
|
Use the substitution mx + n = 1/ t . |
|
|
|
