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Integrate each of the given functions.$$\int_{1}^{e} \frac{3 d u}{u\left[1+(\ln u)^{2}\right]}$$

$\frac{3 \pi}{4}$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 6

Inverse Trigonometric Forms

Integrals

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:44

Evaluate each definite int…

02:00

01:00

00:46

05:52

Evaluate $\int \frac{(\ln …

02:35

Use substitution to find e…

00:55

02:15

Evaluate the following int…

00:29

Evaluate the indefinite in…

07:57

Calculate the integral.

we want to evaluate the following definite integral. The integral from one to E three D U over U times one plus Ellen's where'd you? This question is testing our knowledge of integration techniques in single variable calculus in particular testing our newfound ability to use inverse. You're gonna match up integral. So we have to in such integral are left integral. One is integral to you over a square and a few square equals arts. And you're a pussy on the right to states the integral to you over a squared plus B squared is one over A. Are you over april? See we see that are integral match in the form of two. So we have to now figure out you do um A are you as L M U R D u S t U over U and R equals one. So are integral has an extra factor of three that we must carry over to the solution. Thus we evaluate the integral as three times in trouble. Do you ever you Over one. Radio is three arc tangent. Ellen you from each one or Three times. They are changing 1 -3 times, are Changin zero, so in parentheses as follows.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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