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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Integrate $\frac{3(1 - x)^{3} - 2}{1 - x}$ with respect to $x$.</span></div></li></ol>

Integrate $\frac{3(1 - x)^{3} - 2}{1 - x}$ with respect to $x$.

Integration of Power Functions

Integration of Reciprocal Linear Functions

SCGS 4AM Prelim 2022

Integration

<p>Integrate the following expressions with respect to $x$.</p>
<ol class="abc-list"><li data-list-item-id="item-1770456207213-kvbmf61cb" data-list-item-path="item-1770456207213-kvbmf61cb"><div class="list-item-paragraph">${\displaystyle\displaystyle\int 2\pi \sin \left( \frac{2ex+3}{4} \right) \mathrm{d}x}$</div></li><li data-list-item-id="item-1770456207708-wm5uwy771" data-list-item-path="item-1770456207708-wm5uwy771"><div class="list-item-paragraph">${\displaystyle\displaystyle\int\frac{5-37x}{37x} \ \mathrm{d}x}$</div></li><li data-list-item-id="item-1770456208233-8j99a55ge" data-list-item-path="item-1770456208233-8j99a55ge"><div class="list-item-paragraph">${\displaystyle\int(3+x)\frac{7(3+x)+4}{(3+x)} \ \mathrm{d}x}$</div></li></ol>

Integrate the following expressions with respect to $x$.

Integrable Forms of Trigonometric Functions

<p>${\displaystyle\displaystyle\int \frac{5\sqrt[3]{x} + 7x^3 + \sqrt{x}}{2x^4} \ \mathrm{d}x}$</p>

${\displaystyle\displaystyle\int \frac{5\sqrt[3]{x} + 7x^3 + \sqrt{x}}{2x^4} \ \mathrm{d}x}$

<p>${\displaystyle\displaystyle\int \frac{2x^4 - 8x^3 + \sqrt{x}}{(\sqrt{x})^3} \ \mathrm{d}x}$</p>

${\displaystyle\displaystyle\int \frac{2x^4 - 8x^3 + \sqrt{x}}{(\sqrt{x})^3} \ \mathrm{d}x}$

<p>Integrate the following expressions with respect to $x$.</p>
<ol class="abc-list"><li data-list-item-id="item-1770453687881-orj56nz0s" data-list-item-path="item-1770453687881-orj56nz0s"><div class="list-item-paragraph">$\displaystyle\displaystyle\int \frac{x^2+2x+5}{(x+1)^3}\,\mathrm{d}x$</div></li><li data-list-item-id="item-1770453689007-nnf3cjqgd" data-list-item-path="item-1770453689007-nnf3cjqgd"><div class="list-item-paragraph">$\displaystyle\displaystyle\int \frac{\sqrt{5-x}+7}{\sqrt{5-x}}\,\mathrm{d}x$</div></li></ol>

<p>Integrate the following expressions with respect to $x$.</p>
<ol class="abc-list"><li data-list-item-id="item-1770453070678-60sk31jpg" data-list-item-path="item-1770453070678-60sk31jpg"><div class="list-item-paragraph">$\displaystyle\displaystyle\int \frac{1}{5x} \,\mathrm{d}x$</div></li><li data-list-item-id="item-1770453071436-1ul76qylg" data-list-item-path="item-1770453071436-1ul76qylg"><div class="list-item-paragraph">$\displaystyle\displaystyle\int \frac{7}{2x-5} \,\mathrm{d}x$</div></li></ol>

<p>Integrate the following expressions with respect to $x$:</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{5}{6x} \, \mathrm{d}x$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{1}{4x-3} \, \mathrm{d}x$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{8+(4x-3)^5}{(4x-3)^6} \, \mathrm{d}x$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{5}{2-5x} \, \mathrm{d}x$</span></div></li></ol>

Integrate the following expressions with respect to $x$:

$\displaystyle\displaystyle \displaystyle\int \frac{5}{6x} \, \mathrm{d}x$

$\displaystyle\displaystyle \displaystyle\int \frac{1}{4x-3} \, \mathrm{d}x$

$\displaystyle\displaystyle \displaystyle\int \frac{8+(4x-3)^5}{(4x-3)^6} \, \mathrm{d}x$

$\displaystyle\displaystyle \displaystyle\int \frac{5}{2-5x} \, \mathrm{d}x$

<p>Integrate the following expressions with respect to $x$:</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{1}{3x} \, \mathrm{d}x$</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{5}{3x-1} \, \mathrm{d}x$</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-content"><span class="list-item-text">$\displaystyle\displaystyle \displaystyle\int \frac{3-(2x+1)^2}{(2x+1)^3} \, \mathrm{d}x$</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">$\displaystyle\displaystyle \displaystyle\int \frac{\sqrt{3-x}+5}{\sqrt{3-x}^{3}} \, \mathrm{d}x$</div></li></ol>

$\displaystyle\displaystyle \displaystyle\int \frac{1}{3x} \, \mathrm{d}x$

$\displaystyle\displaystyle \displaystyle\int \frac{5}{3x-1} \, \mathrm{d}x$

$\displaystyle\displaystyle \displaystyle\int \frac{3-(2x+1)^2}{(2x+1)^3} \, \mathrm{d}x$

Math Question Bank