How to find ∫ tanx dx - Integration - Diploma Maths - 2

TL;DR

Learn how to find the integration of tan(x) using a key result and simplifying the expression.

Transcript

click the bell icon to get latest videos from Ikeda hello friends in this video we are going to see how to find the integration of tonics let us start let us consider integral tan X DX as I now to find integration of tan X we are going to use one of the important results that we have already seen few problems in the previous videos out of that one ... Read More

Key Insights

• 🤩 Splitting tan(x) as sin(x)/cos(x) helps in finding its integral using a key result.
• 🤘 Adjusting for the negative sign in the numerator is necessary when integrating tan(x).
• 😑 The integral of tan(x) can be expressed as log|cos(x)| or log|sec(x)|, depending on the form chosen.
• 🆘 Understanding the derivative of cos(x) as -sin(x) helps simplify the integral of tan(x).
• ❓ Applying the property for integrating f'(x)/f(x) is essential in finding the integral of tan(x).
• 😑 Recognizing that 1/cos(x) is equivalent to sec(x) allows for an alternative expression of the integral.
• 😀 The constant C represents the constant of integration and can be added to the result of the integral.

Questions & Answers

Q: How can we find the integration of tan(x)?

To find the integration of tan(x), we can split it as sin(x)/cos(x). Using the property for integrating f'(x)/f(x), the integral simplifies to log|cos(x)| + C.

Q: How do we adjust for the negative sign in the integration of tan(x)?

The derivative of cos(x) is -sin(x), so to adjust for the negative sign in the numerator, we write a minus sign outside the integration. This simplifies the integral to -log|cos(x)| + C.

Q: Can we express the integral of tan(x) using the secant function?

Yes, 1/cos(x) is equal to sec(x). So, the integral of tan(x) can be written as log|sec(x)| + C.

Q: What is the result of the integral of tan(x)?

The result of the integral of tan(x) is log|sec(x)| + C.

Summary & Key Takeaways

• The video explains how to find the integration of tan(x) using a key result involving the derivative of the denominator.

• By splitting tan(x) as sin(x)/cos(x), adjusting for a negative sign, and applying the integration property, the integral simplifies to log|cos(x)|.

• Using the identity 1/cos(x) = sec(x), the final result of the integral is log|sec(x)| + C.