How to integrate $$\int\left(10x^{20}+2x^{19}+3x^{9}+100x^{2}+20x+98\right)dx$$ any hint is welcome.

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    $\begingroup$ Use linearity of the integral and $\int x^n dx = \frac{x^{n+1}}{n+1}+\mathrm{const}$. $\endgroup$
    – J.R.
    Apr 16, 2014 at 18:51
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    $\begingroup$ Don't get impressed by the long sum or high exponents. Just follow the rule stated above. $\endgroup$
    – user88595
    Apr 16, 2014 at 18:56
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  • $\begingroup$ I've deleted a bunch of comments. Please keep comments on-topic, and don't edit this question except to add or clarify details. $\endgroup$ Apr 16, 2014 at 21:02

1 Answer 1


Hint: $$\int\color{darkmagenta}{10x^{20}}+\color{blue}{2x^{19}}+\color{green}{3x^{9}}+\color{red}{100x^{2}}+\color{fuchsia}{20x}+\color{darkorange}{98}\,\mathrm dx\\ =\color{darkmagenta}{\int10x^{20}}\,\mathrm dx+\color{blue}{\int2x^{19}}\,\mathrm dx+\color{green}{\int3x^{9}}\,\mathrm dx+\color{red}{\int100x^{2}}\,\mathrm dx+\color{fuchsia}{\int20x}\,\mathrm dx+\color{darkorange}{\int98}\,\mathrm dx \\\,\\ =\ldots\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad\,\,\,\,\qquad\quad\qquad\quad\,\,\, $$


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