Natural Logarithms Differentiation & Integration

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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

What should be used for u in the integral?

• no u needed
• 4t²
• t³
• 1/4t²

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

What should be assigned to u in the integral?

• 2x²

• sin (2x²)

• 5x

• no u needed

Tags

CCSS.HSF.TF.B.5

∫ 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

∫(5+ln(-2x))⁴∕(x) dx

• ⅚(5+ln(-2x))⁶+C
• ⅘(5+ln(-2x))⁵+C
• ⅕(5+ln(-2x))⁵+C
• ½(5+ln(-2x))⁶+C

What method would you use here?

• antiderivatives
• u-substitution
• integration by parts
• slope fields

This can be integrated using u-substitution. What should "u" equal in this integral?

• x

• (lnx)/x

• lnx

• sin(lnx)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

For u-substitution, what should be used for u here:
∫ (tan⁴xsec²x)dx

• tanx
• tan⁴x
• no u needed
• tanxsecx

For u-substitution what should be "du" in this integral?

• tanxsecx dx
• secx dx
• sec²x dx
• tanx dx

Tags

CCSS.HSA.SSE.A.1

• Intermediate Value Theorem
• Rolle's Theorem
• Average Rate of Change
• Average Value of f

Tags

CCSS.HSF.IF.B.6