Integration as Reverse of Differentiation

JEE Main Mathematics · Indefinite Integration · 3 questions, latest first

• If ∫((1-5 cos^2 x)/(sin^5 x cos^2 x)) d x=f(x)+C, where C is the constant of integration, then f((π)/6)-f((π)/4) is equal to202628 January, Shift 1 · Q20
• For α, β, γ, δ ∈ N, if ∫((x/e)^2 x+(e/x)^2 x) log_e x d x=1/(α)(x/e)^β x-1/(γ)(e/x)^δ x+C, where e=Σ_n=0^∞ 1/(n!) and C is…202310 April, Shift 2 · Q10
• The integral ∫((x/2)^x+(2/x)^x) log_2 x d x is equal to20238 April, Shift 2 · Q10