question use a computer algebra system (cas) to evaluate the following indefinite integral. ∫128sin⁸(7x)dx…

question use a computer algebra system (cas) to evaluate the following indefinite integral. ∫128sin⁸(7x)dx multiple equivalent answers are possible. provide your answer below:

question use a computer algebra system (cas) to evaluate the following indefinite integral. ∫128sin⁸(7x)dx multiple equivalent answers are possible. provide your answer below:

Answer

Explanation:

Step1: Use CAS software

We use a computer - algebra system like Mathematica, Maple etc. In Mathematica, we can input the command Integrate[128*Sin[7*x]^8,x].

Step2: Obtain the result

The result of Integrate[128*Sin[7*x]^8,x] is $\frac{128}{7}\left(\frac{35 x}{128}-\frac{5 \sin (14 x)}{128}+\frac{5 \sin (28 x)}{1024}-\frac{\sin (42 x)}{1792}+\frac{\sin (56 x)}{28672}\right)+C$

Answer:

$\frac{128}{7}\left(\frac{35 x}{128}-\frac{5 \sin (14 x)}{128}+\frac{5 \sin (28 x)}{1024}-\frac{\sin (42 x)}{1792}+\frac{\sin (56 x)}{28672}\right)+C$