Integration Problem - Can Someone Help?

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In summary, the conversation is discussing an integration problem involving hyperbolic functions. The approach of using f'(x)/f(x) was attempted but not successful. The conversation then continues with discussing the integration steps and suggests that the integration can be completed using a substitution method.
  • #1
mahmoud shaaban
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Can someone help with this problem, i tried to solve it
using f'(x)/f(x) but couldn't figure it out.View attachment 5909
 

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  • #2
Hi mahmoud shaaban and welcome to MHB! :D

$$\begin{align*}\int\dfrac{6\sinh(x)\cosh^2(x)+\sinh(x)}{\cosh^3(x)+\cosh(x)}\,dx&=\int\tanh(x)\left(\dfrac{5\cosh^2(x)}{\cosh^2(x)+1}+1\right)\,dx \\
&=5\int\dfrac{\cosh(x)\sinh(x)}{\cosh^2(x)+1}\,dx+\int\tanh(x)\,dx\end{align*}$$

Can you continue?
 
  • #3
mahmoud shaaban said:
[tex]\displaystyle \int \frac{6\sinh x\cosh^2x + \sinh x}{\cosh^3x + \cosh x}\,dx [/tex]

[tex]\text{We have: }\;\int \left(\frac{3\sinh x\cosh^2\!x + \sinh x}{\cosh^3\!x + \cosh x} + \frac{3\sinh x\cosh^2\!x}{\cosh^3\!x + \cosh x}\right)\,dx [/tex]

. . . [tex]=\;\int\left(\frac{3\sinh x\cosh^2\!x + \sinh x}{\cosh^3\!x + \cosh x} +\frac{3\sinh x \cosh x}{\cosh^2\!x + 1} \right)\,dx [/tex]

. . . [tex]=\;\int \frac{3\sinh x\cosh^2\!x + \sinh x}{\cosh^3\!x + \cosh x}\,dx \;+\; \frac{3}{2}\int\frac{2\sinh x\cosh x}{\cosh^2\!x+1}\,dx[/tex]

Can you finish it now?
 

FAQ: Integration Problem - Can Someone Help?

1) What is an integration problem?

An integration problem is a mathematical problem that involves finding the integral of a given function. This involves calculating the area under the curve of the function, which can be a challenging task.

2) Why do people need help with integration problems?

Integration problems can be complex and require a deep understanding of calculus and mathematical concepts. Many people struggle with these types of problems and may need assistance from someone who is knowledgeable in this area.

3) How can someone help with an integration problem?

Someone who is skilled in calculus and integration can provide guidance and assistance with solving integration problems. They can offer explanations, tips, and techniques for solving these types of problems.

4) What are some common techniques for solving integration problems?

Some common techniques for solving integration problems include substitution, integration by parts, and using trigonometric identities. It is important to have a strong understanding of these techniques in order to successfully solve integration problems.

5) Is it cheating to get help with an integration problem?

No, it is not cheating to get help with an integration problem. Seeking assistance from someone who is knowledgeable in this area can help you learn and understand the concepts better. However, it is important to fully understand the solution and not just copy it without understanding the process.

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