How do you integrate x3√144−x2?

1 Answer
Jim H
Aug 23, 2015

Use substitution with u=144−x2.

Explanation:

∫x3√144−x2dx

Let u=144−x2, so that du=−2xdx and x2=144−u

∫x3√144−x2dx=∫x2√144−x2 xdx

=−12∫x2√144−x2 (−2x)dx

=−12∫144−u√u du

=−12∫(144√u−√u) du

=−12∫(144u−12−u12) du

=−12[288u12−23u32]+C

=−144(144−x2)12+13(144−x2)32+C

=−144√144−x2+13(√144−x2)3+C

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