Test: Integration III - Challenging

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Question 1:   Solve integral ( 5 cos( x ) )d( cos( x ) )
F( x )= 5 cos( x ) ln( 5 )
F( x )= 5 cos( x ) +C
F( x )= 5 cos( x ) ln( 5 ) +C
F( x )=5cos( x )+C
Question 2:   Find the antiderivative of the function f( x )= cos 2 ( 7x )
F( x )= 1 2 ( x+ 1 14 ×sin( 14x ) )+C
F( x )=x+ 1 14 ×sin( 14x )+C
F( x )= 1 2 ( x+sin( 14x ) )+C
F( x )= 1 2 ( x+sin( x ) )+C
Question 3:   Find the antiderivative of the function f( x )= 8 1+9 x 2
F( x )= 8 3 arctan( x 3 )+C
F( x )=8arctan( 3x )+C
F( x )= 8 3 arctan( 3x )+C
F( x )= 1 3 arctan( 3x )+C
Question 4:   Calculate 0 π ( 1 cos 2 ( x 4 ) )dx
-3
π
5
4
Question 5:   Find the antiderivative of the function f( x )=5x+1 that passes via point ( 2;5 )
F( x )= 5 x 2 2 +x-7
F( x )= 5 x 2 2 +x-3
F( x )= 5 x 2 2 +x
F( x )= 5 x 2 2 +x+7
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