Integral of Polynomials

\int (9 x^{8} + x^{7} - 8 x^{6} + 5 x^{5} + 6 x^{4} + 3 x^{3} - 8 x - 3) d x

=

\int 9 x^{8} d x + \int x^{7} d x + \int -8 x^{6} d x + \int 5 x^{5} d x + \int 6 x^{4} d x + \int 3 x^{3} d x + \int -8 x d x + \int -3 d x

=

9 \int x^{8} d x + \int x^{7} d x - 8 \int x^{6} d x + 5 \int x^{5} d x + 6 \int x^{4} d x + 3 \int x^{3} d x - 8 \int x d x - 3 \int 1 d x

=

9 (\frac{1}{9} x^{9}) + (\frac{1}{8} x^{8}) - 8 (\frac{1}{7} x^{7}) + 5 (\frac{1}{6} x^{6}) + 6 (\frac{1}{5} x^{5}) + 3 (\frac{1}{4} x^{4}) - 8 (\frac{1}{2} x^{2}) - 3 (x) + C

=

x^{9} + \frac{1}{8} x^{8} - \frac{8}{7} x^{7} + \frac{5}{6} x^{6} + \frac{6}{5} x^{5} + \frac{3}{4} x^{4} - 4 x^{2} - 3 x + C

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