Integral of Polynomials

\int (-4 x^{3} + 8 x^{2} + x) d x

=

\int -4 x^{3} d x + \int 8 x^{2} d x + \int x d x

=

- 4 \int x^{3} d x + 8 \int x^{2} d x + \int x d x

=

- 4 (\frac{1}{4} x^{4}) + 8 (\frac{1}{3} x^{3}) + (\frac{1}{2} x^{2}) + C

=

- x^{4} + \frac{8}{3} x^{3} + \frac{1}{2} x^{2} + C

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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)