Evaluate I = ∫₀^(π/4) log(1 + tan x) dx
Evaluate the definite integral of log(1+tan x) from 0 to π/4 using King’s property, which turns 1+tan x into 2/(1+tan x) under the substitution x → π/4 − x.
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Evaluate the Integral of cos x/[(4 + sin²x)(5 − 4cos²x)] dx
Step-by-step solution to the integral of cos(x)/[(4+sin²x)(5−4cos²x)] dx, using a sine substitution and partial fractions to reduce it to two arctangent terms.
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If I(m,n)=∫x^(m-1)(1-x)^(n-1)dx, Find I(9,14)+I(10,13)
A beta-function-style JEE Main 2025 integral solved without ever evaluating the integral itself — just substitution, addition, and pattern matching.
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If I = ∫96x²cos²x/(1+eˣ)dx = π(απ²+β), Find (α+β)²
A JEE Main 2025 definite integral solved using the King’s property trick for limits symmetric about zero, avoiding a direct, messier computation.