Please solve this integral

extan1xdx\int \mathrm{e}^x tan^{-1}x\mathrm{d}x

#Calculus

Note by Krishna Jha
7 years, 11 months ago

No vote yet
3 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Here tan1xtan^{-1}x is the inverse tangent function and can also be written as arctan(x)arctan(x).

Krishna Jha - 7 years, 11 months ago

Take z=arctan(x), then take dz =dx/(1+x^2)=dx/(1+tan^2z)=dx/(sec^2x)..................so dx=dz(sec^2z)...............so the integral reduces to [ integral e^(tan(z)) sec^2(z)) dz.....now substitute y=tan(z).....and tada u'll ger it!! Hope u understand it.........

(N.B..here sec^2(z) means sec squared z.................okay?)

Piyal De - 7 years, 11 months ago

Log in to reply

Man... You missed out a z....the integral is etanzz(sec2z)dz\int\mathrm{e}^{tanz}z(sec^{2}z)\mathrm{d}z.... coz there was an arctan(x)arctan(x) there... u have to back substitute arctan(x)=zarctan(x)=z... Now please solve this further... :-P..

Krishna Jha - 7 years, 11 months ago

Log in to reply

My bad!!!...Sorry sorry...

Piyal De - 7 years, 11 months ago

You should check this.

Aditya Parson - 7 years, 11 months ago

Log in to reply

Pls tell me how to solve this integral with the Ei(x) function..

Krishna Jha - 7 years, 11 months ago

12eiiEi(i+x)12ieiEi(i+x)+extan1(x)\frac{1}{2} e^i i \text{Ei}(-i+x)-\frac{1}{2} i e^{-i} \text{Ei}(i+x)+e^x \tan ^{-1}(x)

Louie Tan Yi Jie - 7 years, 11 months ago

Log in to reply

HOW???

Krishna Jha - 7 years, 11 months ago

Log in to reply

Wolfram | Alpha

Jimmi Simpson - 7 years, 11 months ago

Why not use integration by parts

Tanmay Bhoite - 7 years, 11 months ago

Log in to reply

Use it and show me how do u do it...

Krishna Jha - 7 years, 11 months ago
×

Problem Loading...

Note Loading...

Set Loading...