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πŸ”₯ Day 92 β€” Can you solve this? Evaluate the integral: Integral from 0 to 1 of (ln x)^2 dx It looks tricky β€” but there’s a clean parameter move πŸ”§ Differentiate ∫ x^a dx with respect to a, or do IBP twice and it collapses. πŸ‘‰ The trick? Start with βˆ«β‚€¹ x^a dx = 1/(a 1), differentiate twice to generate (ln x)^2, then set a = 0 πŸ‘€ Would you get the exact value before time runs out? ⏱️ πŸ’­ Drop your answer below πŸ‘‡ βœ… Full step-by-step solution is already on my page. ➑️ Follow for the rest of 100 Math
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πŸ”₯ Day 117 β€” Can you solve this? Evaluate the integral (a > 0, b β‰₯ 0): βˆ«β‚€^∞ e^(βˆ’a x) · sin(bx) / x dx It looks tough β€” but a parameter derivative makes it collapse πŸ“‰ Differentiate with respect to b, use the Laplace transform of cos(bx), then integrate back. πŸ‘‰ Hint: Fβ€²(b) = βˆ«β‚€^∞ e^(βˆ’a x) cos(bx) dx = a/(a² b²). Integrate in b and use F(0) = 0 to nail the constant πŸ‘€ Would you land the exact expression before time runs out? ⏱️ πŸ’­ Drop your answer below πŸ‘‡ βœ… Full step-by-step solution is already
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