Calcule cada uma das integrais abaixo. (a) ∫ 1 1− x2 dx (b) ∫ x+ 4 x2 + 5x− 6 dx (c) ∫ x x2 − 2x− 3 dx (d) ∫ x3 x2 + 2x+ 1 dx (e) ∫ 1 (x2 − 1)2 dx ...

(a) ∫ 1/(1-x²) dx = arctan(x) + C (b) ∫ (x+4)/(x²+5x-6) dx = ln|x-1| - ln|x+6| + C (c) ∫ x/(x²-2x-3) dx = (1/2)ln|x-3| - (1/2)ln|x+1| + C (d) ∫ x³/(x²+2x+1) dx = (1/2)x² - 2x + 5ln|x+1| + C (e) ∫ 1/(x²-1)² dx = (1/4)ln| (x-1)/(x+1) | + (1/2)[(1/ (x-1)²) - (1/ (x+1)²)] + C (f) ∫ 1/[(x+1)(x²+1)] dx = (1/2)ln|x²+1| - ln|x+1| + C (g) ∫ e^x/(e^(2x)+3e^x+2) dx = (1/2)ln|e^x+1| - (1/2)ln|e^x+2| + C (h) ∫ cos(x)/(sin²(x)+sin(x)-6) dx = (1/2)ln|sin(x)-2| - (1/2)ln|sin(x)+3| + C (i) ∫ 1/(x³-x) dx = (1/2)ln|x| - (1/4)ln|x²-1| + C (j) ∫ (2x+3)/(x²(4x+1)) dx = (1/2)ln|x²+1| - (1/4)ln|x| - (1/4)ln|4x+1| + C (k) ∫ (x³+5x²-4x-20)/(x²+3x-10) dx = (1/2)x² + 6x - 2ln|x-2| + ln|x+5| + C (l) ∫ x²/(x²-x-6) dx = x - 2ln|x-3| + ln|x+2| + C