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Integrate each of the given functions.$$\int 6 x^{2} e^{x^{3}} d x$$

$2 e^{x^{3}}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Missouri State University

University of Michigan - Ann Arbor

Boston College

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mhm. We want to evaluate the following the integral or rather the indefinite integral of six X squared E. Execute. This question is testing our knowledge of methods of integration. We've already learned about the power rule as well as the log arrhythmic integration in this problem, we're being asked to use exponential integration which states that the integral of E. To the U d U n E D U plus C. So if we identify you and D. U. And are given integral, we should be able to plug into the exponential integration rules to solve easily. You is whatever raised to the power of E. So in this problem let us execute. So you was executed in the U. S. Three X squared dx. We see the r integral has an extra factor of two for six X squared dx. Which means we have to carry this over to the final solution. So are integral is to integrate into the U. D. U. Or to E to the X. Cubed plus C. Which is a constant of integration.

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