25.1 a) integral x*sin(x) dx from -pi to pi b) integral ln x dx from 1 to e c) integral sqrt(1-x^2)/x^2 dx from 1/2 to 1 d) integral x^3*cos(x/2) dx from 0 to pi e) integral e^x*sin x dx from 0 to pi f) integral x*(sin x) * (cos x) dx from -pi to pi 25.2 a) integral (3x^4+6x^2+1)/(x^2+1) dx from -1 to 1 b) integral (x^2+3)/(x^2+3x) dx from 1 to 2 c) integral (x^3+1)/(x^3-x^2) dx from 2 to 4 d) integral (x^3+x+2)/((x-1)(x+1)) dx from 2 to 3 f) integral (x^3+1)/(x(x^2-1)) dx from 2 to 3 25.3 a) integral (x^2+1)/(x^2-4) dx from 0 to 1 b) integral sin(x/2)/cos^2(x/2) dx from 0 to pi/2 c) integral (x+4)*sqrt(x^2+8x+7) dx from -1 to 0 e) integral sqrt(cos x - cos^3 x) dx from -pi/2 to pi/3 f) integral (x+3)/(x^2+4) dx from 0 to 2 f) integral x^x*(1 + ln x) dx from 1 to 3 i) integral x^2*arctan x dx from 0 to 1