Indefinite Integral of 7^lnx

TL;DR

Learn how to find the indefinite integral of 7 raised to the natural log of X.

Transcript

consider this problem what is the indefinite integral of 7 raised to the natural log of X feel free to try this problem now what we need to do is adjust this equation we could replace 7 with e raised to the ln 7 the base of the natural log is e and these two they cancel given a 7 so for instance 5 is equal to e raised to the ln 5 so that's our firs... Read More

Key Insights

• ✊ The indefinite integral of 7 raised to the natural log of X can be found by replacing 7 with e raised to the ln 7 and applying the power rule.
• 👻 Switching the exponents allows for easier manipulation of the equation.
• 🧑‍💻 The final answer involves multiplying 7 raised to the natural log of X with X and dividing by 1 plus the natural log of 7, and adding a constant of integration.
• ✊ The power rule is applicable to finding the indefinite integral of a variable raised to a constant.

Questions & Answers

Q: What is the indefinite integral being evaluated in this problem?

The indefinite integral being evaluated is 7 raised to the natural log of X.

Q: How is the equation simplified in the first step?

The equation is simplified by replacing 7 with e raised to the ln 7.

Q: What is the significance of switching the exponents?

Switching the exponents allows for the application of the power rule, making it easier to find the indefinite integral.

Q: What is the final answer to the problem?

The final answer to the problem is 7 raised to the natural log of X times X divided by 1 plus the natural log of 7, plus a constant of integration.

Summary & Key Takeaways

• The problem involves finding the indefinite integral of 7 raised to the natural log of X.

• By replacing 7 with e raised to the ln 7, the equation can be simplified.

• Switching the exponents and using the power rule, the indefinite integral is determined to be 7 raised to the natural log of X times X divided by 1 plus the natural log of 7, plus a constant of integration.