<ol class="i-list"><li data-list-item-id="imported-item-block-0-item-0" data-list-item-path="imported-item-block-0-item-0"><div class="list-item-paragraph">Find \(\int \frac{1}{x}(\ln x)^5 \,\mathrm{d}x\).<span class="inline-marks">[2]</span></div></li><li data-list-item-id="imported-item-block-0-item-1" data-list-item-path="imported-item-block-0-item-1"><div class="list-item-paragraph">Use the substitution \(u = e^{2x}\) to find \(\int \frac{e^{2x}}{1 + 4e^{4x}} \,\mathrm{d}x\).<span class="inline-marks">[4]</span></div></li><li data-list-item-id="imported-item-block-0-item-2" data-list-item-path="imported-item-block-0-item-2"><div class="list-item-paragraph">Evaluate \(\int_0^2 \frac{e^{2x}}{1 + 4e^{4x}} \,\mathrm{d}x\), giving the answer correct to \(3\) decimal places.<span class="inline-marks">[1]</span></div></li></ol>

Find \(\int \frac{1}{x}(\ln x)^5 \,\mathrm{d}x\).

Use the substitution \(u = e^{2x}\) to find \(\int \frac{e^{2x}}{1 + 4e^{4x}} \,\mathrm{d}x\).

Evaluate \(\int_0^2 \frac{e^{2x}}{1 + 4e^{4x}} \,\mathrm{d}x\), giving the answer correct to \(3\) decimal places.

2018 TGM P1 Q4

2018 TGM P1 Q4

Solution:

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