Integration by Substitution

JEE Main Mathematics · Indefinite Integration · 8 questions, latest first

• If ∫(1/x+1/x^3)(√[23](3 x^-24+x^-26)) d x=-(α)/(3(α+1))(3 x^β+x^γ)^((α+1)/(α))+C, x>0,(α, β, γ ∈ Z), where C is the constant of…20257 April, Shift 2 · Q24
• If ∫ ((√(1+x^2)+x)^10)/((√(1+x^2)-x)^9) d x=1/(m)((√(1+x^2)+x)^n(n √(1+x^2)-x))+C where C is the constant of integration and m, n…20254 April, Shift 2 · Q25
• Let f(x)=∫ x^3 √(3-x^2) d x. If 5 f(√2)=-4, then f(1) is equal to20253 April, Shift 1 · Q18
• Let I(x)=∫ 6/(sin^2 x(1- cot x)^2) d x. If I(0)=3, then I((π)/12) is equal to20248 April, Shift 1 · Q10
• If ∫ (sin^(3/2) x+ cos^(3/2) x)/(√(sin^3 x cos^3 x sin (x-θ))) d x=A √(cos θ tan x- sin θ)+B √(cos θ- sin θ cot x)+C, where C is…202429 January, Shift 2 · Q10
• The integral ∫ ((x^8-x^2) d x)/((x^12+3 x^6+1) tan^-1(x^3+1/x^3)) is equal to:202427 January, Shift 2 · Q11
• Let I(x)=∫ ((x+1))/(x(1+x e^x)^2) d x, x>0. If lim_x → ∞ I(x)=0, then I(1) is equal to20238 April, Shift 1 · Q11
• If ∫ √(sec 2 x-1) d x=α log_e| cos 2 x+β+√(cos 2 x(1+ cos 1/(β) x))|+ constant, then β-α is equal to ____.202330 January, Shift 2 · Q87