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1∫0ex⋅x(1+x)2dx is equal to |
Answer» <span class="mjx-chtml" id="MathJax-Element-1-Frame"><span class="mjx-math" id="MJXc-Node-277876"><span class="mjx-mrow" id="MJXc-Node-277877"><span class="mjx-mstyle" id="MJXc-Node-277878"><span class="mjx-mrow" id="MJXc-Node-277879"><span class="mjx-munderover" id="MJXc-Node-277880"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.258em; padding-top: 0.141em; padding-left: 0.81em;"><span class="mjx-texatom" id="MJXc-Node-277885" style=""><span class="mjx-mrow" id="MJXc-Node-277886"><span class="mjx-mn" id="MJXc-Node-277887"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-op"><span class="mjx-mo" id="MJXc-Node-277881" style="vertical-align: 0.001em; padding-right: 0.388em;"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 1.109em; padding-bottom: 1.109em;">∫</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.025em;"><span class="mjx-texatom" id="MJXc-Node-277882" style=""><span class="mjx-mrow" id="MJXc-Node-277883"><span class="mjx-mn" id="MJXc-Node-277884"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-mstyle MJXc-space1" id="MJXc-Node-277888"><span class="mjx-mrow" id="MJXc-Node-277889"><span class="mjx-mfrac" id="MJXc-Node-277890"><span class="mjx-box MJXc-stacked" style="width: 3.661em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 3.661em; top: -1.37em;"><span class="mjx-mrow" id="MJXc-Node-277891"><span class="mjx-msubsup" id="MJXc-Node-277892"><span class="mjx-base"><span class="mjx-mi" id="MJXc-Node-277893"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" id="MJXc-Node-277894" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space2" id="MJXc-Node-277895"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-mi MJXc-space2" id="MJXc-Node-277896"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-denominator" style="width: 3.661em; bottom: -1.093em;"><span class="mjx-mrow" id="MJXc-Node-277897"><span class="mjx-mo" id="MJXc-Node-277898"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn" id="MJXc-Node-277899"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2" id="MJXc-Node-277900"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2" id="MJXc-Node-277901"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-msubsup" id="MJXc-Node-277902"><span class="mjx-base"><span class="mjx-mo" id="MJXc-Node-277903"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" id="MJXc-Node-277904" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-line" style="border-bottom: 1.3px solid; top: -0.296em; width: 3.661em;"></span></span><span class="mjx-vsize" style="height: 2.462em; vertical-align: -1.093em;"></span></span></span></span><span class="mjx-mi" id="MJXc-Node-277905"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi" id="MJXc-Node-277906"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span> is equal to<br> | |