Integration

(1) $∫ x^n dx = {x^{n+1}}/{n + 1} + c$

(2) $∫ 1/x dx = log|x| + c$

(3) $∫a^x dx = {a^x}/{loga} + c$

(4) $∫e^x dx = e^x + c$

(5) $∫sinx dx = – cosx + c$

(6) $∫cosx dx = sinx + c$

(7) $∫tanx dx = log |secx| + c$

(8) $∫cotx dx = log |sinx| + c$

(9) $∫secx dx = log |secx + tanx| + c$

(10) $∫cosecx dx = log |cosecx – cotx| + c$

(11) $∫sec^2 x dx = tanx + c$

(12) $∫cosec^2 x = – cotx + c$

(13) $∫secx tanx dx = secx + c$

(14) $∫cosecx cotx dx = – cosecx + c$

(15) $∫1/{√{1 – x^2}} dx = sin^{-1}x + c = – cos^{-1}x + c$

(16) $∫1/{1 + x^2} dx = tan^{-1}x + c = – cot^{-1}x + c$

(17) $∫{1}/{x√{x^2 – 1}} dx = sec^{-1}x + c = – cosec^{-1}x + c$

(18) $∫1/{√{a^2 – x^2}} dx = sin^{-1}(x/a) + c$

(19) $∫1/{a^2 + x^2} dx = 1/a tan^{-1}(x/a)$

(20) $∫1/{x√{x^2 – a^2}} dx = 1/a sec^{-1} (x/a) + c$