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Sunday, June 2, 2013

More Integration Procedures, 9

Category: Integral Calculus, Trigonometry

"Published in Suisun City, California, USA"

Evaluate


Solution:

Consider the given equation above


There are two functions in the given equation which are x3 and sin x, respectively. If

 then

If
then

By applying the integration by parts, we have







Since the second term at the right side of the equation have two functions which are x2 and cos x, then we have to apply the integration by parts again. If

then

If
then

Again, by applying the integration by parts, we have







Therefore, the first integration by parts becomes







Since the second term at the right side of the equation have two functions which are x and sin x, then we have to apply the integration by parts again. If

then

If
then

Again, by applying the integration by parts, we have

 


 



Therefore, the final answer is