JEE Main Mathematics — Indefinite Integration Previous-Year Questions

Let I(x)=∫ 3 d x(4 x+6) (4 x²+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…

Let f(t)=∫ (1- ( e t )1- ( e t ) ) d t, t>1. If f (eⁱ / ² )=-eⁱ / ² and f (eⁱ / ⁴ )=α eⁱ / ⁴, then α equals

Let f(x)=∫ (2-x² ) · ex(√(1+x))(1-x)³ / ² ~d x. If f(0)=0, then f ((1)/(2) ) is equal to:

Let f(x)=∫ d xx ⁽⁽²⁾/⁽³⁾ⁱght⁾+2 x ⁽⁽¹⁾/⁽²⁾ⁱght⁾ be such that f(0)=-26+24 e(2). If f(1)=a+b e(3), where a, b Z, then a+b…

Let f(x) = ∫ ((16x + 24)/(x² + 2x - 15) ) dx. If f(4) = 14 (3) and f(7) = (2α · 3β), α, β N, then α + β is equal to:

If ∫( x)⁽⁻¹¹⁾/⁽²⁾( x)⁽⁻⁵⁾/⁽²⁾ d x= -p₁q₁( x)⁽⁹⁾/⁽²⁾-p₂q₂( x)⁽⁵⁾/⁽²⁾-p₃q₃( x)⁽¹⁾/⁽²⁾+p₄q₄( x)⁽⁻³⁾/⁽²⁾+C, where pi and qi…

If ∫ (√(1+x²)+x )¹⁰ (√(1+x²)-x )⁹ d x= (1)/(m) ( (√(1+x²)+x )ⁿ (n √(1+x²)-x ) )+C where C is the constant of integratio…

If f(x)=∫ 1x¹ / ⁴ (1+x¹ / ⁴ ) d x, f(0)=-6, then f(1) is equal to :

If ∫ e^x (x ⁻¹ x√(1-x²)+ ⁻¹ x (1-x² )³ / ²+(x)/(1-x²) ) d x=g(x)+C, where C is the constant of integration, then g ((1)…

If ∫ 2 x²+5 x+9√(x²+x+1) ~d x=x √(x²+x+1)+α √(x²+x+1)+β e |x+(1)/(2)+√(x²+x+1) |+C, where C is the constant of integrat…