<ol class="abc-list"><li><div class="list-item-paragraph">Find $\int{\frac{\cos x}{\sqrt[3]{\sin x}}}\,\mathrm{d}x$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Using the substitution $x=1-{{\mathrm{e}}^{u}}$, find $\int{\frac{1}{1-{{\mathrm{e}}^{u}}}\,\mathrm{d}u}$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">Find $\int{x\ln \left( x+1 \right)\,\mathrm{d}x}$, where $x>-1$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-paragraph">Write down constants $A$ and $B$ such that, for all values of $x$, $x=A\left( 2x+2 \right)+B$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Hence, find $\int{\frac{x}{{{x}^{2}}+2x+2}\,\mathrm{d}x}$.</div><p style="text-align: right;">[4]</p></li></ol></li></ol>

Find $\displaystyle\displaystyle \int{\frac{\cos x}{\sqrt[3]{\sin x}}}\,\mathrm{d}x$.

Using the substitution $x=1-{{\mathrm{e}}^{u}}$, find $\displaystyle\displaystyle \int{\frac{1}{1-{{\mathrm{e}}^{u}}}\,\mathrm{d}u}$.

Find $\displaystyle\displaystyle \int{x\ln \left( x+1 \right)\,\mathrm{d}x}$, where $x>-1$.

2023 JPJC Promo Q13

2023 JPJC Promo Q13

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