Question

7.1 EXERCISES 1-2 Evaluate the integral using integration by parts with the indicated choices of \( u \) and \( d v \). 1. \( \int x e^{2 x} d x ; \quad u=x, d v=e^{2 x} d x \) 2. \( \int \sqrt{x} \ln x d x ; \quad u=\ln x, d v=\sqrt{x} d x \)

          7.1 EXERCISES

1-2 Evaluate the integral using integration by parts with the indicated choices of \( u \) and \( d v \).
1. \( \int x e^{2 x} d x ; \quad u=x, d v=e^{2 x} d x \)
2. \( \int \sqrt{x} \ln x d x ; \quad u=\ln x, d v=\sqrt{x} d x \)

7.1 EXERCISES

1-2 Evaluate the integral using integration by parts with the indicated choices of u and d v.
1. ∫ x e^2 x d x ; u=x, d v=e^2 x d x
2. ∫√(x)ln x d x ; u=ln x, d v=√(x) d x

Added by Aaron M.

Calculus for AP

Jon Rogawski & Colin Adams 3rd Edition

Chapter 7

Instant Answer

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The formula is: \[ \int u \, dv = uv - \int v \, du \] Show more…

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7.1 EXERCISES 1-2 Evaluate the integral using integration by parts with the indicated choices of \( u \) and \( d v \). 1. \( \int x e^{2 x} d x ; \quad u=x, d v=e^{2 x} d x \) 2. \( \int \sqrt{x} \ln x d x ; \quad u=\ln x, d v=\sqrt{x} d x \)