Integration by Substitution and Inverse Trigonometry Functions

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

• e^x

• 1+e^x

• (1+e^x)^(1/2)

• (e^x)^(1/2)

Solve for u-substitution: ∫x(x²-2)¹⁵ dx

• ((x²-2)¹⁶)/32 + C
• (x²-2)¹⁶ + C
• (x³-3)¹⁵ + C

∫(3x⁴+2)⁴(12x³)dx

• ½(3x⁴+2)⁴+C
• (3x⁴+2)⁴+C
• ⅕(3x⁴+2)⁵+C
• ⅓(3x⁴+2)⁶+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

∫ 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 

∫ 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

What should be assigned to u in the integral?

• 2x²

• sin (2x²)

• 5x

• no u needed

What should be used for u in the integral?

• no u needed
• 4t²
• t³
• 1/4t²

• ln(2x²+6) + C
• ln(2x²+6)(4x) + C
• 1/(2x²+6) + C
• 1/(2x²+6)² + C

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C