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  <question type="stack">
    <name>
      <text>13.1.2.5 Find integrals</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Integrate each of the following functions with respect to \(x\), i.e. for each function \(f(x)\) calculate \(\int f(x) \ \mathrm{d}x\) and enter this in the answer box:</p>
<ol class="HELM_parts">
<li><p>if \(f(x)={@exp1@}\) then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li> 
<li><p>if \(f(x)={@exp2@}\)&nbsp;then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li> 
<li><p>if \(f(x)= \displaystyle {@exp3@}\) then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li> 
<li><p>if \(f(x)= \displaystyle {@exp4@}\) then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p></li> 
<li><p>if \(f(x)={@exp5@}\)&nbsp;then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans5]] [[validation:ans5]] [[feedback:prt5]]</p></li> 
<li><p>if \(f(x)={@exp6@}\)&nbsp;then \(\displaystyle{\int f(x)\ \mathrm{d}x=}\) [[input:ans6]] [[validation:ans6]] [[feedback:prt6]]</p></li> 
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<h4 class="HELM_solution"><span style="color: rgb(73, 80, 87); font-size: 0.9375rem;">Remember that \(\dfrac{1}{x^n}\) can be written as \(x^{-n}\) and \(\sqrt{x}\) can be written as \(x^{\frac{1}{2}}\). So:</span><br></h4>
<ol class="HELM_parts">
    <li>\( \displaystyle \int {@exp1@}\ \mathrm{d}x= {@ta1@}.\)</li>
    <li>\(&nbsp;\displaystyle \int {@exp2@}\ \mathrm{d}x = {@ta2@}.\)</li>
    <li>\( \displaystyle \int {@exp3@}\ \mathrm{d}x= {@ta3@}.\)</li>
    <li>\( \displaystyle \int {@exp4@}\ \mathrm{d}x = {@ta4@}.\)</li>
    <li>\( &nbsp;\displaystyle \int{@exp5@}\ \mathrm{d}x = {@ta5@}.\)</li>
    <li>\( &nbsp;\displaystyle \int{@exp6@}\ \mathrm{d}x = {@ta6@}.\)</li>
</ol>]]></text>
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    <stackversion>
      <text>2020120600</text>
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      <text>nn : 2+rand(9);
mm:rand_with_prohib(2,7,[nn]);
kk: nn-1;
dn : rand(10)+5;

simp:false;
exp1: x^nn;
exp2: x^(1/2);
exp3: x^(-mm);
exp4: 1/x^(kk);
exp5: dn;
exp6: e^(4*x);


ta1: ev(int(exp1, x),simp) + c; 
ta2: ev(int(exp2, x),simp) + c; 
ta3: ev(int(exp3, x),simp) + c; 
ta4: ev(int(exp4, x),simp) + c;
ta5: ev(int(exp5, x),simp) + c; 
ta6: ev(int(exp6, x),simp) + c;</text>
    </questionvariables>
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    <questionnote format="moodle_auto_format">
      <text>\[ \int{@exp1@}\mathrm{d}x = {@ta1@}, \quad \int{@exp2@}\mathrm{d}x ={@ta2@}, \quad \int{@exp3@}\mathrm{d}x ={@ta3@}\]
\[\int{@exp4@}\mathrm{d}x = {@ta4@}, \quad \int{@exp5@}\mathrm{d}x = {@ta5@}, \quad \int{@exp6@} \mathrm{d}x= {@ta6@}\]</text>
    </questionnote>
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      <text><![CDATA[<p><span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.<br></p>]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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