Integral of Polynomials

\int (4 x^{8} + 6 x^{7} - 10 x^{6} + 5 x^{5} - 2 x^{4} - 7 x^{3} + 4 x^{2} - 9 x + 10) d x

=

\int 4 x^{8} d x + \int 6 x^{7} d x + \int -10 x^{6} d x + \int 5 x^{5} d x + \int -2 x^{4} d x + \int -7 x^{3} d x + \int 4 x^{2} d x + \int -9 x d x + \int 10 d x

=

4 \int x^{8} d x + 6 \int x^{7} d x - 10 \int x^{6} d x + 5 \int x^{5} d x - 2 \int x^{4} d x - 7 \int x^{3} d x + 4 \int x^{2} d x - 9 \int x d x + 10 \int 1 d x

=

4 (\frac{1}{9} x^{9}) + 6 (\frac{1}{8} x^{8}) - 10 (\frac{1}{7} x^{7}) + 5 (\frac{1}{6} x^{6}) - 2 (\frac{1}{5} x^{5}) - 7 (\frac{1}{4} x^{4}) + 4 (\frac{1}{3} x^{3}) - 9 (\frac{1}{2} x^{2}) + 10 (x) + C

=

\frac{4}{9} x^{9} + \frac{3}{4} x^{8} - \frac{10}{7} x^{7} + \frac{5}{6} x^{6} - \frac{2}{5} x^{5} - \frac{7}{4} x^{4} + \frac{4}{3} x^{3} - \frac{9}{2} x^{2} + 10 x + C

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