Integration By Parts

Step 1: Integration by parts.
To solve $%5Cint%20x%5E2%20%5Cln%20x%20%5C%2C%20dx$ , we apply integration by parts. Let: $u%20%3D%20%5Cln%20x%20%5Ctext%7Band%7D%20dv%20%3D%20x%5E2%20%5C%2C%20dx$ Then, $du%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%5C%2C%20dx$ and $v%20%3D%20%5Cfrac%7Bx%5E3%7D%7B3%7D$ .

Step 2: Applying the formula.
The integration by parts formula is: $%5Cint%20u%20%5C%2C%20dv%20%3D%20uv%20-%20%5Cint%20v%20%5C%2C%20du$ Substitute the values: $%5Cint%20x%5E2%20%5Cln%20x%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5Cln%20x%20-%20%5Cint%20%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7Bx%7D%20%5C%2C%20dx$ Simplifying the second integral: $%3D%20%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5Cln%20x%20-%20%5Cfrac%7B1%7D%7B3%7D%20%5Cint%20x%5E2%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5Cln%20x%20-%20%5Cfrac%7Bx%5E3%7D%7B9%7D%20%2B%20C$

Step 3: Conclusion.
The correct answer is (A) $%5Cfrac%7Bx%5E3%7D%7B3%7D%20%5Cln%20x%20-%20%5Cfrac%7Bx%5E3%7D%7B9%7D%20%2B%20C$ .

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Integration By Parts

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs