Integral of Polynomials

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

=

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

=

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

=

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

=

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

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