Integral of Polynomials

\int (x^{5} + 8 x^{4} + 3 x^{2} + 8 x - 9) d x

=

\int x^{5} d x + \int 8 x^{4} d x + \int 3 x^{2} d x + \int 8 x d x + \int -9 d x

=

\int x^{5} d x + 8 \int x^{4} d x + 3 \int x^{2} d x + 8 \int x d x - 9 \int 1 d x

=

(\frac{1}{6} x^{6}) + 8 (\frac{1}{5} x^{5}) + 3 (\frac{1}{3} x^{3}) + 8 (\frac{1}{2} x^{2}) - 9 (x) + C

=

\frac{1}{6} x^{6} + \frac{8}{5} x^{5} + x^{3} + 4 x^{2} - 9 x + C

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