Solution Outline

When faced with integrals that involve multiplying two simpler functions, integration by parts can be a useful technique. The initial term in our integral features an inverse trigonometric function along with a reciprocal function.

According to the LIATE rule, we prioritize which function to designate as 'u' based on their categories: logarithmic, inverse trigonometric, algebraic, trigonometric, and exponential functions.

To begin our integration by parts for the first component, we set up as follows:

With this arrangement, we can insert our functions into the formula below.

Before we proceed, can you anticipate where this might lead us? Take a moment to reflect on the original question if needed!

Next, let’s evaluate the first integral:

Returning to our original problem, the latter two terms effectively cancel each other out!

Thus, our final result is simply:

Isn’t that remarkable? Here’s a delightful ice cream as a reward for your efforts!

And that concludes our problem-solving adventure. What were your thoughts while working through this? I’d love to hear from you in the comments!

Math Puzzles Collection

Explore a curated selection of intriguing math puzzles on Medium, encompassing Algebra, Geometry, Calculus, Number Theory, and beyond. Share these with your friends!

The first video showcases a remarkable integral challenge from the JEE Advanced calculus exam, providing valuable insights into tackling such problems.

The second video presents top questions from Integral Calculus aimed at Class 12 students preparing for the JEE Advanced exam.

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