Integration by Partial Fractions

JEE Main Mathematics · Indefinite Integration · 2 questions, latest first

• Let f(x)=∫((16 x+24)/(x^2+2 x-15)) d x. If f(4)=14 log_e(3) and f(7)= log_e(2^α · 3^β), α, β ∈ N, then α+β is equal to:20262 April, Shift 2 · Q19
• Let f(x)=∫ (2 x)/((x^2+1)(x^2+3)) d x. If f(3)=1/2( log_e 5- log_e 6), then f(4) is equal to202325 January, Shift 1 · Q69