Integration of Irrational Functions

JEE Main Mathematics · Indefinite Integration · 7 questions, latest first

• Let f(x)=∫ (d x)/(x^(2/3)+2 x^(1/2)) be such that f(0)=-26+24 log_e(2). If f(1)=a+b log_e(3), where a, b ∈ Z, then a+b is equal…202628 January, Shift 2 · Q18
• Let I(x)=∫ (3 d x)/((4 x+6)(√(4 x^2+8 x+3))) and I(0)=(√3)/4+20. If I(1/2)=(a √2)/b+c, where a, b, c ∈ N, gcd(a, b)=1, then a+b+c…202623 January, Shift 2 · Q19
• If f(x)=∫ 1/(x^1 / 4(1+x^1 / 4)) d x, f(0)=-6, then f(1) is equal to:202528 January, Shift 2 · Q19
• Let I(x)=∫ (d x)/((x-11)^(11/13)(x+15)^(15/13)). If I(37)-I(24)=1/4(1/(b^(1/13))-1/(c^(1/13))), b, c ∈ N, then 3( b+c) is equal to202523 January, Shift 1 · Q18
• If ∫ 1/(√[5]((x-1)^4(x+3)^6)) d x=A((α x-1)/(β x+3))^B+C, where C is the constant of integration, then the value of α+β+20 AB is…20248 April, Shift 2 · Q26
• Let f(x)=∫ (d x)/((3+4 x^2) √(4-3 x^2)),|x|<2/(√3). If f(0)=0 and f(1)=1/(α β) tan^-1((α)/(β)), α, β>0, then α^2+β^2 is equal to…202315 April, Shift 1 · Q26
• Let I(x)=∫ √((x+7)/x) d x and I(9)=12+7 log_e 7. If I(1)=α+7 log_e(1+2 √2), then α^4 is equal to ____.202312 April, Shift 1 · Q27