Find \(\displaystyle\displaystyle \displaystyle\int\nolimits_{0}^{4} \mathrm{e}^{|x-1|} \, \mathrm{d

Question

Find $\displaystyle\displaystyle \displaystyle\int\nolimits_{0}^{4} \mathrm{e}^{|x-1|} \, \mathrm{d}x$, leaving your answer in exact form.[4] Find $\displaystyle\displaystyle \displaystyle\int \sin^{2} 3x + \tan^{2} 3x \, \mathrm{d}x$.[3] Use the substitution $x = u^{6}$, where $u > 0$, to find $\displaystyle\displaystyle \displaystyle\int \frac{1}{\sqrt{x} + \sqrt[3]{x}} \, \mathrm{d}x$.[5]

Accepted Answer

(a) ${e^3 + e - 2}$ (b) ${-\frac{1}{12}\sin 6x + \frac{1}{3}	an 3x - \frac{1}{2}x + C}$ (c) ${2\sqrt{x} - 3\sqrt[3]{x} + 6\sqrt[6]{x} - 6\ln\left(\sqrt[6]{x} + 1ight) + C}$

2025 EJC P1 Q10

2025 EJC P1 Q10