$\"\"$

The integral is $\"\"$ .

The series is in the form of $\"\"$ .

The power series form of $\"\"$ is $\"\"$ .

The power series form of $\"\"$ .

$\"\"$

Apply integral on each side.

$\"\"$

$\"\"$ .

Therefore, the power series is $\"\"$ . $\"\"$

The series is $\"\"$

Consider $\"\"$ .

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

If $\"\"$ then $\"\"$ .

$\"\"$

The series is converges for $\"\"$ .

$\"\"$ .

The radius of convergence is $\"\"$ .

Therefore, the power series is $\"\"$ and $\"\"$ .

$\"\"$

The power series for $\"\"$ is $\"\"$ .

$\"\"$

The function is $\"\"$ .

Tabulate the values for different values of $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

The values of $\"\"$ .

$\"\"$ .

Using power series $\"\"$ .

$\"\"$

$\"\"$ .