Test: Integration II - Ambitious

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Question 1:   Find the antiderivative of the function f( x )= ( 2x+5 ) 2
F( x )= x 3 3 +5 x 2 +25x+C
F( x )= 4 x 3 3 +5 x 2 +25x
F( x )= x 3 3 + x 2 2 +25+C
F( x )= 4 x 3 3 +5 x 2 +25x+C
Question 2:   Find the antiderivative of the function f( x )= ( 2 6x ) 2
F( x )= 2 12x 12ln( 2 )
F( x )= 2 12x 12ln( 2 ) +C
F( x )= 2 12x ln( 2 ) +C
F( x )= 2 12x +C
Question 3:   Find the antiderivative of the function f( x )= 1 cos 2 ( 2x )
F( x )= 1 2 tan( 2x )+C
F( x )= 1 2 tan( 2x )
F( x )= 1 2 tan( x )+C
F( x )=tan( 2x )+C
Question 4:   Find the equation of integral for the area of the shaded region:

S= ( x+1 )dx
S= ( ( x+1 )- x 2 )dx
S= ( x 2 )dx
S= ( x 2 -( x+1 ) )dx
Question 5:   Find the antiderivative of the function f( x )= 1 21+ x 2
F( x )= 1 21 arctan( x 21 )+C
F( x )=arctan( x 21 )+C
F( x )= 1 21 arctan( x )+C
F( x )= 1 21 arctan( x 21 )
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