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We are given:

we applied the integration by parts rule , the second time for integration of

2 x * sin 2x by taking u = x and v = 2 Sin2x.

finally, the integration involved just Cos 2x.

So we are able reduce the power of x 1 each time we applied the rule.

we applied the integration by parts rule , the second time for integration of

2 x * sin 2x by taking u = x and v = 2 Sin2x.

finally, the integration involved just Cos 2x.

So we are able reduce the power of x 1 each time we applied the rule.