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<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li data-list-item-id="item-1785847295068-a8zsodu8n" data-list-item-path="item-1785847295068-a8zsodu8n"><div class="list-item-paragraph"><p>$\int \frac{1}{4-9x} \mathrm{d}x$</p></div></li><li data-list-item-id="item-1785847297899-q5i719d1n" data-list-item-path="item-1785847297899-q5i719d1n"><div class="list-item-paragraph"><p>$\int \frac{1}{4-9x^2} \mathrm{d}x$</p></div></li><li data-list-item-id="item-1785847299155-yqtbf39aq" data-list-item-path="item-1785847299155-yqtbf39aq"><div class="list-item-paragraph"><p>$\int \frac{x}{4-9x^2} \mathrm{d}x$</p></div></li><li data-list-item-id="item-1785847299892-ahmcmu9lj" data-list-item-path="item-1785847299892-ahmcmu9lj"><div class="list-item-paragraph"><p>$\int \frac{x+3}{4-9x^2} \mathrm{d}x$</p></div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="5"><li data-list-item-id="item-1785847311604-x9nrhgskw" data-list-item-path="item-1785847311604-x9nrhgskw"><div class="list-item-paragraph"><p>$\int \frac{x^2}{4-9x^2} \mathrm{d}x$</p></div></li><li data-list-item-id="item-1785847312891-wh8uh9njz" data-list-item-path="item-1785847312891-wh8uh9njz"><div class="list-item-paragraph"><p>$\int \frac{x}{\sqrt{4-9x^2}} \mathrm{d}x$</p></div></li><li data-list-item-id="item-1785847314123-msl6ulyl3" data-list-item-path="item-1785847314123-msl6ulyl3"><div class="list-item-paragraph"><p>Find $\int \frac{x+2}{\sqrt{1-8x-4x^2}} \mathrm{d}x$.</p></div></li><li data-list-item-id="item-1785847314843-jeq1sfc48" data-list-item-path="item-1785847314843-jeq1sfc48"><div class="list-item-paragraph"><p>Find $\int \frac{x}{x^2+4x+7} \mathrm{d}x$.</p></div></li></ol></div></div></div>

Integration by Splitting the Numerator

Integration by the Reverse Chain Rule

Integrals Involving Long Division

Indefinite Integrals by Inspection

Logarithmic Integrals of $\frac{f'(x)}{f(x)}$

Integration by Completing the Square

Standard Integrals with Quadratic Denominators

Techniques of Integration

<p>$\displaystyle\int{{{15}^{x}}\mathrm{d}x}$</p>

$\displaystyle\displaystyle \displaystyle\int{{{15}^{x}}\mathrm{d}x}$

<p>$\displaystyle\int{{{7}^{x}}}\mathrm{ d}x$</p>

$\displaystyle\displaystyle \displaystyle\int{{{7}^{x}}}\mathrm{ d}x$

<ol class="abc-list" start="2"><li><div class="list-item-paragraph">It is given that&nbsp;$\,\mathrm{f}(x)=\frac{1}{x-1}$.</div><ol class="i-list"><li><div class="list-item-paragraph">On separate diagrams, sketch the graphs of $y=\mathrm{f}\left( \left| x \right| \right)$ and $y=\left| \mathrm{f}\left( x \right) \right|$. 	<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Without the use of graphing calculator, find the exact value of the constant $a$, where&nbsp;$0&lt;a&lt;1$, for which  	$\left| \displaystyle\int_{\text{  }-\frac{1}{2}\ }^{\text{ }\frac{1}{2}}{\text{f (}\left| x \right|)\ \mathrm{d}x} \right|=\displaystyle\int_{\text{  }0\ }^{\text{ }a}{\left| \text{f (}x) \right|\ \mathrm{d}x}$.	<span class="inline-marks">[4]</span></div></li></ol></li></ol>

Integrals involving Modulus Functions

2013 ACJC P2 Q4 

Applications of Integration

<ol class="abc-list" start="3"><li><div class="list-item-paragraph">Evaluate $\displaystyle\displaystyle \displaystyle\int{\,\frac{1}{\sqrt{x}{{\left( 1+\sqrt{x} \right)}^{2}}}\mathrm{d}x}$.</div></li><li><div class="list-item-paragraph">Evaluate $\displaystyle\displaystyle \displaystyle\int{\frac{4}{{{e}^{-x}}-1}\,\mathrm{d}x}$.</div></li><li><div class="list-item-paragraph">Evaluate $\displaystyle\displaystyle \displaystyle\int{{{\left( \sin x+2\cos x \right)}^{2}}}\,\mathrm{d}x$.</div></li><li><div class="list-item-paragraph">Evaluate $\displaystyle\displaystyle \displaystyle\int{\sec \left( 2x-5 \right)\mathrm{ d}x}$.</div></li></ol>

Evaluate $\displaystyle\displaystyle \displaystyle\int{\,\frac{1}{\sqrt{x}{{\left( 1+\sqrt{x} \right)}^{2}}}\mathrm{d}x}$.

Evaluate $\displaystyle\displaystyle \displaystyle\int{\frac{4}{{{e}^{-x}}-1}\,\mathrm{d}x}$.

Evaluate $\displaystyle\displaystyle \displaystyle\int{{{\left( \sin x+2\cos x \right)}^{2}}}\,\mathrm{d}x$.

Evaluate $\displaystyle\displaystyle \displaystyle\int{\sec \left( 2x-5 \right)\mathrm{ d}x}$.

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