Integrals of the Form ∫e^x[f(x) + f'(x)] dx

JEE Main Mathematics · Indefinite Integration · 4 questions, latest first

• Let f(t)=∫((1- sin ( log_e t))/(1- cos ( log_e t))) d t, t>1. If f(e^π / 2)=-e^π / 2 and f(e^π / 4)=α e^π / 4, then α equals202624 January, Shift 1 · Q19
• Let f(x)=∫ ((2-x^2) · e^x)/((√(1+x))(1-x)^3 / 2) d x. If f(0)=0, then f(1/2) is equal to:202623 January, Shift 1 · Q18
• If ∫ e^x((x sin^-1 x)/(√(1-x^2))+(sin^-1 x)/((1-x^2)^3 / 2)+x/(1-x^2)) d x=g(x)+C, where C is the constant of integration, then…202522 January, Shift 2 · Q20
• If I(x)=∫ e^sin^2 x( cos x sin 2 x- sin x) d x and I(0)=1, then I((π)/3) is equal to202310 April, Shift 1 · Q8