Question $7$

Evaluate the following integral: ${\displaystyle \underset{3}{\overset{\frac{13}{4}}{}}}ta{n}^{3}xse{c}^{3}xdx$

$-\frac{1}{120}(16+7\sqrt[\phantom{2}]{2})$

$-\frac{1}{120}(16-7\sqrt[\phantom{2}]{2})$

$-\frac{2}{15}(1+\sqrt[\phantom{2}]{2})$

$-\frac{2}{15}(1-\sqrt[\phantom{2}]{2})$