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Question

# Use a computer algebra system to (a) find or evaluate the integral and (b) graph two antiderivatives. (c) Describe the relationship between the graphs of the antiderivatives. $\int_{0}^{5} x^{4}\left(25-x^{2}\right)^{3 / 2} d x$

Solution

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$\int_0^5 x^4(25-x^2)^{3/2} \ dx$

For the indefinite integral you can type into WolframAlpha:

 integral of (x^4 (25 - x^2)^(3/2) ) dx


which results in:

$\dfrac{1}{128}(1171875 \arcsin \dfrac{x}{5} - x\sqrt{25-x^2} (16x^6-600x^4+1250x^2+46875)) + C$

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