Exam

Exam: find the solutions of these integrals:


a) 4√x + 4ln(√x + 1) + k

b) 4√x - 4ln(√x - 1) + k

c) 2/(1 + √x)

d) 4√x - 4ln(√x + 1) + k



a) x2/2 (lnx + 1/2) + k

b) x2/2 (lnx - 1/2) + k

c) x2/2 (lnx - 1) + k

d) x2 (lnx - 1/2) + k



a) 1/2(sin2x - sin2x) + k

b) sin2x + sin2x + k

c) 1/2(sin2x + sin2x) + k

d) sin2x - sin2x + k



a) x3/3 - x2 + 4x - 9·ln|x+2| + k

b) x3 - x2 + 4x - 9·ln|x+2| + k

c) x3/3 + x2 + 4x - 9·ln|x+2| + k

d) x3/3 - x2 + 4x + ln|x+2| + k



a) arctan2x + 4·ln(1 + x2) + k

b) arctanx + ln(1 + x2) + k

c) arctanx - 4·ln(1 + x2) + k

d) arctanx + 4·ln(1 + x2) + k



a) 7ln|x - 1| - 5ln|x - 2| + 8(x-2) + k

b) 2ln|x - 1| + (4/3)ln|x - 2| - 1/3(x-2) + k

c) (1/3)ln|x - 1| + (4/3)ln|x - 2| + 1/3(x-2) + k

d) (-1/3)ln|x - 1| + (4/3)ln|x - 2| + 1/3(x-2) + k



a) arctan(2/3)x + k

b) (1/6)arctan(2/3)x + k

c) arctan(3/2)x + k

d) (1/6)arctan(3/2)x + k



a) ln|x + 1| - ln|x| + 2/x + k

b) ln|x + 1| - ln|x| - 2/x + k

c) ln|x + 1| + 4ln|x| - 1/x + k

d) 5ln|x + 1| - ln|x| - 3/x + k



a) -2e√x + k

b) (1/2)e√x + k

c) 2e√x + k

d) -(1/2)e√x + k



a) 3sin3x + k

b) (-1/3)sin3x + k

c) (1/3)sin3x + k

d) -3sin3x + k


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