Problem 51456. Compute an improper integral of a ratio of algebraic functions

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; "><span style="">Write a function to compute the following integral:</span></span></div><div style="block-size: 45.0833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5417px; text-align: left; transform-origin: 384px 22.5417px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})" style="width: 193px; height: 45px;" width="193" height="45"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; "><span style="">where </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "><span style=""> and </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; "><span style=""> are positive real numbers. You may not use </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">integral</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; "><span style=""> or </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">quad</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Problem 51456. Compute an improper integral of a ratio of algebraic functions

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Problem 51456. Compute an improper integral of a ratio of algebraic functions

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