- #1
Lorena_Santoro
- 22
- 0
\( \int\frac{dx}{1+tanx} \)
Thank you very much!Klaas van Aarsen said:Substitute $u=\tan x$, which means $x=\arctan u$ and $dx=\frac{1}{1+u^2}\,du$.
Follow up with partial fraction decomposition.
$$\begin{align}\int\frac{dx}{1+\tan x}&=\int \frac{1}{1+u}\cdot\frac{1}{1+u^2}\,du
=\int\Big(\frac{\frac 12}{1+u}+\frac{-\frac 12 u +\frac 12}{1+u^2}\Big)\,du
=\frac 12\ln(1+u)-\frac 14\ln(1+u^2)+\frac 12\arctan u + C \\
&=\frac 12\ln(1+\tan x)-\frac 14\ln(1+\tan^2 x) +\frac 12 x + C\end{align}$$
When approaching a research study, it is important to first define the research question or problem. From there, you can determine the appropriate research design, data collection methods, and statistical analysis techniques. It is also important to consider any ethical considerations and potential biases that may impact the study.
When analyzing data, it is important to first clean and organize the data. This includes checking for missing values, outliers, and any other data errors. From there, you can choose the appropriate statistical analysis techniques based on the research question and data type. It is also important to interpret the results and communicate them effectively.
When troubleshooting a scientific experiment, it is important to first identify the specific issue or problem. From there, you can review the experimental design and protocol to determine if any steps were missed or if there were any errors. It may also be helpful to consult with colleagues or experts in the field for their insights and suggestions.
When writing a scientific paper, it is important to first have a clear understanding of the research question and results. From there, you can organize the paper into sections such as introduction, methods, results, and discussion. It is important to use clear and concise language, provide evidence to support your findings, and follow the appropriate formatting and citation guidelines.
When presenting scientific findings, it is important to first consider the audience and their level of understanding of the topic. From there, you can choose the appropriate format for the presentation, such as a conference talk or poster presentation. It is important to use visual aids and clear language to effectively communicate the findings and their significance.