$\"\"$

\

The integral is $\"\"$ .

\

(a)

\

For $\"\"$ , $\"\"$ .

\

Solve the integral using integration by parts.

\

Formula for integration by parts : $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Consider $\"\"$ .

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$ .

\

Substitute corresponding values in integration by parts.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

For $\"\"$ , $\"\"$ .

\

Solve the integral using integration by part.

\

Formula for integration by parts : $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Consider $\"\"$ .

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$ .

\

Substitute corresponding values in integration by parts.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

For $\"\"$ , $\"\"$ .

\

Solve the integral using integration by parts.

\

Formula for integration by parts : $\"\"$ .

\

Consider $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Consider $\"\"$ .

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$ .

\

Substitute corresponding values in integration by parts.

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(b)

\

Observe the pattern :

\

$\"\"$ , $\"\"$ and

\

$\"\"$ .

\

$\"\"$ , $\"\"$ .

\

$\"\"$

\

(a) $\"\"$ , $\"\"$ and

\

$\"\"$ .

\

(b) $\"\"$ , $\"\"$ .