Integral of Polynomials

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

=

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

=

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

=

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

=

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

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