Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on integration.
∫x^3ex^4 dx.

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]:                                                        

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u:                                                                                                             [u] Basic Power Rule:                                                                                    

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]:                 [Integral] U-Substitution:                                                                               [Integral] Exponential Integration:                                                               [u] Back-Substitute:                                                                                      

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration