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    <name>
      <text>13.1.3.4 Using rules of integration</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Find</p>
<ol class="HELM_parts">
<li><p>\({\displaystyle \int ({@exp1@})\ \mathrm{d}x}=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li> 
<li><p>\({\displaystyle \int{@exp2@}\ \mathrm{d}x}=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>
<li><p>\({\displaystyle \int{@exp3@}\ \mathrm{d}x}=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>
<li><p>\({\displaystyle \int{@exp4@}\ \mathrm{d}x}=\) [[input:ans4]] [[validation:ans4]] [[feedback:prt4]]</p></li>
<li><p>\({\displaystyle \int{@exp5@}\ \mathrm{d}x}=\) [[input:ans5]] [[validation:ans5]] [[feedback:prt5]]</p></li>
</ol>]]></text>
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    <generalfeedback format="html">
      <text><![CDATA[<p>[[facts:calc_int_linearity_rule]]<br></p>

<ol class="HELM_parts">
    <li>\(\begin{aligned} \displaystyle \int ({@exp1@})\ \mathrm{d}x &amp;= {@nn@}\displaystyle \int x \ \mathrm{d}x - \displaystyle \int {@exp1_2@} \ \mathrm{d}x, \\ &amp;= {@ta1@}. \end{aligned}\)</li>
    <li>\(&nbsp;\displaystyle \int {@exp2@}\ \mathrm{d}x= {@mm@}\displaystyle \int e^{{@nn@}x} \ \mathrm{d}x = {@ta2@}.\)</li>
    <li>\(\begin{aligned} \displaystyle \int {@exp3@}\ \mathrm{d}x &amp;= \dfrac{1}{{@oo@}} \displaystyle \int \cos(2x) \ \mathrm{d}x + \dfrac{1}{{@oo@}} \displaystyle \int x \ \mathrm{d}x, \\ &amp;= {@int(exp3_1,x)@} + {@int(exp3_2,x)@} + c, \\ &amp;= {@ta3@}.
        \end{aligned}\)
    </li>
    <li>\( \displaystyle \int {@exp4@}\ \mathrm{d}x = {@ta4@}.\)</li>
    <li>\(\begin{aligned} &nbsp;\displaystyle \int{@exp5@}\ \mathrm{d}x &amp;=&nbsp;\int ({@expand(exp5)@})\&nbsp; \mathrm{d}x , \\ &amp;= \int x^2 \ \mathrm{d}x + \int {@2*oo@}x \ \mathrm{d}x + \int {@oo^2@} \ \mathrm{d}x, \\ &amp;= {@ta5@}. \end{aligned}\)</li>
</ol>]]></text>
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    <stackversion>
      <text>2020120600</text>
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    <questionvariables>
      <text>nn : 2+rand(4);
mm:1+rand(3);
oo: rand([1, 3, 5])

exp1: (nn*x-e^x);
ta1: int(exp1, x) + c;

exp2: mm*e^(nn*x);
ta2: int(exp2, x) + c;

exp3: (1/oo)*(x+cos(2*x)); 
ta3: fullratsimp(int(exp3, x)) + c;

exp4: (nn-1)*x^(-2);
ta4: int(exp4, x) + c;

exp5: (x+oo)^2;
ta5: int(exp5, x) + c;

/*For Worked Solution*/
exp1_1: nn*x;
exp1_2: %e^x;

exp3_1: (1/oo)*cos(2*x);
exp3_2: (1/oo)*x;</text>
    </questionvariables>
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    <questionnote format="moodle_auto_format">
      <text>\[ \int ({@exp1@}) \mathrm{d}x= {@ta1@} \quad \int {@exp2@} \mathrm{d}x= {@ta2@} \quad \int {@exp3@} \mathrm{d}x= {@ta3@} \]
\[ \int {@exp4@} \mathrm{d}x = {@ta4@} \quad \int {@exp5@} \mathrm{d}x = {@ta5@} \]</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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