Test: Integration II - Challenging

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Question 1:   Solve integral ( 1 cos 2 ( e x ) )d( e x )
F( x )= e x +C
F( x )=tan( e x )+C
F( x )=tan(x)+C
F( x )=tan( e x )
Question 2:   Find the antiderivative of the function f( x )= cos 2 ( 3x )
F( x )=x+ 1 6 ×sin( 6x )+C
F( x )= 1 2 ( x+ 1 6 ×sin( 6x ) )+C
F( x )= 1 2 ( x+sin( x ) )+C
F( x )= 1 2 ( x+sin( 6x ) )+C
Question 3:   Find the antiderivative of the function f( x )= 5 1+16 x 2
F( x )= 5 4 arctan( 4x )+C
F( x )= 5 4 arctan( 4x )+C
F( x )= 1 4 arctan( 4x )+C
F( x )=5arctan( 4x )+C
Question 4:   Calculate 0 π ( sin( x 3 ) )dx
π
1.5
1
3.5
Question 5:   Find the antiderivative of the function f( x )=9 x 2 -x that passes via point ( 1;1 )
F( x )=3 x 3 - x 2 2 +2
F( x )=3 x 3 - x 2 2 -1.5
F( x )=3 x 3 - x 2 2 -1
F( x )=3 x 3 - x 2 2 +C
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