Basic Integration by Substitution

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

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

∫5 e^5x dx

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

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + 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

∫ e^2x dx

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

What should be used for u in the integral?

• no u needed
• 4t²
• t³
• 1/4t²