5 Multiple Choice 1 point Which of the following functions would be best solved by using integration by parts? \( \int(1 / 3) x^{4} d x \) \( \int x^{2} \sin (10 x) d x \) \( \int x v\left(5+x^{2}\right) d x \) \( \int x^{-1} d x \)

When it comes to integration by parts, you're looking for integrals where you can apply the formula \( \int u \, dv = uv - \int v \, du \). Among the options given, the integral \( \int x^{2} \sin(10x) \, dx \) is best suited for this method. Why? Because you can choose \( u = x^2 \) and \( dv = \sin(10x) \, dx \), making it a classic case for applying integration by parts effectively! On the other hand, the other integrals are either straightforward polynomials, like \( \int (1/3)x^{4} \, dx \), which just requires power rule integration, or presents little room for parts, such as \( \int x^{-1} \, dx \), which is better solved via the natural logarithm. So buckle up, because with integration by parts, you're diving into a realm where functions can dance together in harmony!