MTH 240 Midterm: MTH240 W2017 Midterm 1
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Solution: this is not the only correct solution. by parts [ u = ln(1 x) 1 dv = dx v = x ] t (2t) dt. Ln(1 x) dx = x ln(1 x) + = x ln(1 x) + ( t 1 + 1 t) dt t2 t ln|1 t| + c x x ln|1 x| + c. Solution: these are not the only correct solutions. (1 cos(2 ))2(1 + cos(2 )) d . [sin2 = 1 cos2 = 1. [cos3(2 ) cos2(2 ) cos(2 ) + 1] d . [(1 sin2(2 )) cos(2 ) cos2(2 ) cos(2 ) + 1] d . 2 (1 + cos(4 )) cos(2 ) + 1] d sin(4 ) . [sin2 = 1 sin cos = 1. 8 [ sec d + du ln| sec + tan | ln|2x + 4x2 1| sin2 . 5 d + sec d ] d + sec d ] 8 (1 + tan2 ) sec tan2 .
