$\"\"$

(a) The integration by parts is based on the product rule.

The product rule of derivative : $\"\"$ .

Apply Integrattion on each side.

$\"\"$

Since $\"\"$ .

$\"\"$

$\"\"$ .

Therefore, the integration by parts formula is $\"\"$ .

$\"\"$

The integration by parts formula is $\"\"$ .

Try letting $\"\"$ be the most complicated portion of the integrand that fits a basic integration rule.

The term $\"\"$ will be the remaining factors of the integrand.

The term $\"\"$ is always includes the $\"\"$ of the original integrand.

$\"\"$

(a) The integration by parts is based on the product rule.

(b) The integration by parts formula is $\"\"$ .

Try letting $\"\"$ be the most complicated portion of the integrand that fits a basic integration rule.

The term $\"\"$ will be the remaining factors of the integrand.

The term $\"\"$ is always includes the $\"\"$ of the original integrand.