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The functions $y=e^{x^{3}}$ and $y=x^{3} e^{x^{3}}$ do not have elementary anti-derivatives, but $y=\left(1+3 x^{3}\right) e^{x^{3}}$ does.Evaluate$$\int\left(1+3 x^{3}\right) e^{x^{3}} d x$$

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

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

Techniques of Integration

Section 1

Using Basic Integration Formulas

Integration

Integration Techniques

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University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:50

The functions $ y = e^{x^2…

01:26

Find the derivatives of th…

00:32

Compute the derivative of …

01:43

Find the first and second …

01:01

Make the indicated substit…

00:37

00:53

Use Part 1 of the Fundamen…

00:49

00:56

Find derivatives of the fu…

02:41

look at this won't cause separate out first. Next. And I wouldn't be using the place in my heart for this tax lives. This is Max. You cannot do that thes term into these. Chairman. Get canceled. So we got we wish.

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In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

The functions $ y = e^{x^2} $ and $ y = x^2 e^{x^2} $ don't have elemen…

Find the derivatives of the functions.$$y=x e^{-x}+e^{x^{3}}$$

Compute the derivative of the following functions.$$y=\frac{2 e^{x}+3 e^…

Find the first and second derivatives.$$y=\frac{x^{3}}{3}+\frac{x^{2}}{2…

Make the indicated substitution for an unspecified function $f(x)$.$$u=x…

Compute the derivative of the following functions.$$g(x)=\$$\frac{1-3 x}…

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of …

Find derivatives of the functions defined as follows.$$y=3 e^{2 x^{2}}$$…

Find derivatives of the functions defined as follows.$$y=(x+3)^{2} e^{4 …

08:10

Evaluate the integrals in Exercises $41-60$$$\int_{-\pi / 4}^{\pi / 4} \…

01:58

Evaluate the integrals.$\int \sin ^{5} x d x$

02:54

Find the areas of the surfaces generated by revolving the curves inExerc…

01:04

In Exercises $13-24,$ find the derivative of $y$ with respect to the appropr…

01:57

a. Estimate the value of $$\lim _{x \rightarrow \infty}\left(x-\sqrt{x^{…

05:37

Find the derivative of $y$ with respect to the given independent variable.

00:58

Evaluate the integrals in Exercises $67-74$ in terms of\begin{equation}\…

00:40

Evaluate the integrals.$\int \cos ^{3} x \sin x d x$

Use l'Hopital's rule to find the limits in Exercises $7-50$ .$…

07:01

Evaluate the integrals by using a substitution prior to integration by parts…

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