Integral of Polynomials

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

=

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

=

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

=

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

=

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

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