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  "body": "\n## Statement\n\nLet $n \\ge 0$ be an integer and let $a, b \\in \\mathbb{R}$.\nThen\n$$\\int_a^b x^n \\, dx = \\frac{b^{n+1} - a^{n+1}}{n + 1}.$$\n\n## Remarks\n\nBy the [[power rule|0JZGW75C5Z]], $x^{n+1}/(n + 1)$ is an antiderivative of $x^n$. Apply the [[second fundamental theorem|0XYAFCN0PT]].\nThe same formula holds for each real exponent $r \\ne -1$, on intervals inside $(0, \\infty)$. The case $r = -1$ gives the [[logarithm|0K1N1Y4EGZ]].\nMathlib states it as `integral_pow`.\n\n## Explanations\n\n### L1 human\n\nTo integrate $x^n$, raise the power by one and divide by the new power.\nFor example, $\\int_0^1 x^2 \\, dx = 1/3$.\n",
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