Integration by Substitution

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C
• (3/2)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(-1/2)+C

Tags

CCSS.HSA.APR.A.1

CCSS.HSN.RN.A.2

∫ sin (2x) dx

• cos(2x)+C
• -(1/2)cos(2x)+C
• -cos(2x)+C
• (1/2)cos(2x)+C

∫ 6 x (x² +1 )² dx

• ( x² + 1)³ + C
• 3 ( x² + 1)³ + C
• ( x² + 1)¹ + C
• 6 ( x² + 1)³ + C

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

∫ e^2x dx

• e^2x +C
• 2e^2x + C
• (1/2)e^{x + C}
• (1/2)e^2x +C

Tags

CCSS.HSF.IF.C.8

∫ (2 - x)⁵ dx

• -5 (2 - x )⁴ + C
• ( 2 - x )⁶ + C 
• (1/6) ( 2 - x )⁶ + C 
• -(1/6) ( 2 - x )⁶ + C 

∫ x (x² + 7 )^(1/3) dx 

• (3/4) ( x²+ 7 )^(4/3) + C
• (3/8) ( x²+ 7 )^(4/3) + C 
•  ( x²+ 7 )^(4/3) + C 
• (3/2) ( x²+ 7 )^(4/3) + C 

Tags

CCSS.HSA.APR.A.1

CCSS.HSN.RN.A.2

∫ 2x cos(x²) dx

• sin(2x) + C
• 2 sin ( 2x ) + C 
• (1/2) sin(2x) + C 
• 4 cos(2x ) + C

∫5 e^5x dx

• 25 e^5x + C 
• 5 e^{5x - 1} + C 
• e^5x +  C 
• (1/5) e^5x + C 

∫ g ' ( x ) f (u) dx,    u = g ( x )

• ∫ f ( u ) du
• g ( x ) + C 
• ( 1/ g ( x ) ) g ( x)⁴ + C 
• cannot be determined

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

∫ sec²(x) dx

• sec(x) + C
• sec²(x) + C 
• sin(x)cos(x) + C
• tan(x) + C