Integrals of Transcendental Functions

Evaluate:
∫ x e^-3x² dx

• -⅙ e^-3x²+c
• ⅓ e^-3x²+c
• -⅓ e^-3x²+c
• ⅙ e^-3x²+c

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

Find the derivative:
y=4^x

• y′=4^x
• y′=(lnx)4^x
• y′=(ln4)4^x
• y′=(log4)4^x

What is an antiderivative?

• The opposite of a derivative
• The same as a derivative
• A second derivative
• It always represents velocity.

• A
• B
• C
• D

• e^√x + C

• 2e^√x+C

• ¼ e^√x +C

• ln√x +C

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

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

Which of these can be integrated using u-substitution?

• A

• B

• both

• neither

When using u-substitution to integrate this, what is the u?

• 2x

• e^x

• x²

• none of these

∫5 e^5x dx

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