Integral of Polynomials

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

=

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

=

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

=

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

=

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

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