Evaluate the integrals. $\int \frac{\log _{10} x}{x} d x$
Added by Sherry P.
Step 1
Let $u = \log_{10} x$ and $dv = \frac{1}{x} dx$. Then, $du = \frac{1}{x \ln 10} dx$ and $v = \ln x$. Using the formula for integration by parts, we have: $$\int \frac{\log_{10} x}{x} dx = uv - \int v du$$ $$= \ln x \cdot \log_{10} x - \int \ln x \cdot Show more…
Show all steps
Close
Your feedback will help us improve your experience
Zhumagali Shomanov and 92 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integrals. $$\int x(x-1)^{10} d x$$
Integrals
Indefinite Integrals and the Substitution Method
Evaluate the following integrals. $$\int \frac{d x}{x^{2}-2 x+10}$$
Integration Techniques
Basic Approaches
Evaluate the integrals. \begin{equation}\int_{1 / 10}^{10} \frac{\log _{10}(10 x)}{x} d x\end{equation}
Transcendental Functions
Exponential Functions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD