<p>Integrate the following with respect to \(x\):</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\( \displaystyle \displaystyle\int \sin\left(2x + \frac{\pi}{2}\right) \, \mathrm{d}x \)</div></li><li><div class="list-item-paragraph">\( \displaystyle \displaystyle\int 6\sec^{2} 3x \, \mathrm{d}x \)</div></li><li><div class="list-item-paragraph">\( 
\displaystyle 
\displaystyle\int \mathrm{cosec}\left(\frac{\pi}{4} - 3x\right)\cot\left(\frac{\pi}{4} - 3x\right) \, \mathrm{d}x
\)</div></li></ol>

Integrate the following with respect to \(x\):

\[\displaystyle \displaystyle\int \sin\left(\(2\)x + \frac{\pi}{\(2\)}\right) \, \mathrm{d}x\]

\( \displaystyle \displaystyle \displaystyle\int \sin\left(2x + \frac{\pi}{2}\right) \, \mathrm{d}x \)

\[\displaystyle \displaystyle\int \(6\)\sec^{\(2\)} \(3\)x \, \mathrm{d}x\]

\( \displaystyle \displaystyle \displaystyle\int 6\sec^{2} 3x \, \mathrm{d}x \)

\[\displaystyle \displaystyle\int \mathrm{cosec}\left(\frac{\pi}{\(4\)} - \(3\)x\right)\cot\left(\frac{\pi}{\(4\)} - \(3\)x\right) \, \mathrm{d}x\]

\( 
\displaystyle 
\displaystyle \displaystyle\int \mathrm{cosec}\left(\frac{\pi}{4} - 3x\right)\cot\left(\frac{\pi}{4} - 3x\right) \, \mathrm{d}x
\)

Indefinite integral of simple trigonometric functions

Indefinite integral of simple trigonometric functions