How Can You Verify the Reduction Formula $\int(\ln x)^{n} d x=x(\ln x)^{n}-n \int(\ln x)^{n-1} d x$

question 44

Multiple Choice

How can you verify the reduction formula: $\int(\ln x) ^{n} d x=x(\ln x) ^{n}-n \int(\ln x) ^{n-1} d x$ in one step?

• A)using integration by parts (that is, \(\int u d v=u v-\int v d u\) )with
• \(u=(\ln x)^{n}\) and
• \(d v=d x\) .
• B)using integration by parts (that is, \(\int u d v=u v-\int v d u\) )with
• \(u=(\ln x)^{n-1}\) and
• \(d v=\ln x d x\) .
• C)using the substitution \(w=\ln x\) .

Recognize the mechanisms of oxygen and carbon dioxide transport within the body.

Explain ventilation and its importance in respiratory efficiency.

Understand the physics of breathing in various environments and at different elevations.

Describe the adaptations of respiratory systems to overcome challenges associated with gas solubility and diffusion.

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