Test: Integration I - Challenging

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Question 1:   Solve integral ( 1 1- sin 2 ( 3x ) )d( sin( 3x ) )
F( x )=arcsin( sin( 3x ) )
F( x )=sin( arcsin( 3x ) )+C
F( x )=sin( 3x )+C
F( x )=arcsin( sin( 3x ) )+C
Question 2:   Find the antiderivative of the function f( x )= sin 2 ( 5x )
F( x )= sin 3 ( 5x ) 3 +C
F( x )= 1 2 ( x-sin( 10x ) )+C
F( x )= 1 2 ( x- 1 10 ×sin( 10x ) )+C
F( x )=x- 1 10 ×sin( 10x )+C
Question 3:   Find the antiderivative of the function f( x )= 1 1+5 x 2
F( x )= 1 5 arccot( 5 x )+C
F( x )=5arccot( 5 x )+C
F( x )= 1 5 arccot( x )+C
F( x )= 5 arccot( 5 x )+C
Question 4:   Calculate 0 π ( cos( x 2 ) )dx
2
π
4
1
Question 5:   Find the antiderivative of the function f( x )=8 x 3 +3 x 2 that passes via point ( 1;5 )
F( x )=2 x 4 + x 3 +2
F( x )=2 x 4 + x 3
F( x )=2 x 4 + x 3 +C
F( x )=2 x 4 + x 3 +5
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