Improper integrals

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8) Problem: Examine the improper integral for convergence: \[ \int_{0}^{+\infty} \sin x d x \]

9.3.2.1 Improper integrals

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3) Problem: Investigate the convergence of an improper integral of an unbounded function: \[ \int_{0}^{1} \frac{d x}{1-\sqrt[3]{x}} \]

9.3.2.2 Improper integrals

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al Problem: Examine the improper integral of an unbounded function for convergence: \[ I=\int_{0}^{\frac{1}{8}} \frac{\sin ^{-1}\left(x^{2}+x^{5}\right)}{x \ln ^{2}(1-x)} d x \]

9.3.2.3 Improper integrals

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(2) Problem: Calculate the improper integral or prove its divergence: \[ \int_{e}^{\infty} \frac{d x}{x \ln ^{2} x} \]

9.3.2.4 Improper integrals

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3) Problem: Calculate the improper integral or prove its divergence: \[ \int_{-\infty}^{-3} \frac{x d x}{\left(x^{2}+1\right)^{2}} \]

9.3.2.5 Improper integrals

1.27 $

30 Problem: Calculate the improper integral: \[ \int_{-\infty}^{+\infty} \frac{d x}{x^{2}+2 x+2} \]

9.3.2.6 Improper integrals

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3) Problem: Calculate the improper integral of an unbounded function: \[ \int_{-1}^{1} \frac{x-1}{\sqrt[3]{x^{5}}} d x \]

9.3.2.7 Improper integrals

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3) Problem: Examine the improper integral of the unbounded function for convergence: \[ \int_{0}^{8} \frac{d x}{2 x^{3}+5 \sqrt{x}} \]

9.3.2.8 Improper integrals

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(3) Problem: Examine the improper integral for convergence: \[ \int_{0}^{+\infty} \frac{2 x d x}{1+x^{2}} \]

9.3.2.9 Improper integrals

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Problem: Calculate the improper integral: \[ \int_{0}^{+\infty} \frac{\tan ^{-1}(x-1)}{\sqrt[3]{(x-1)^{4}}} d x \]

9.3.2.10 Improper integrals

2.54 $

Problem: Examine the improper integral for convergence: \[ \int_{0}^{2} \frac{d x}{x} \]

9.3.2.11 Improper integrals

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§ Problem: Examine the improper integral for convergence: \[ \int_{1}^{+\infty} \frac{\ln \cos (1 / x)}{x} d x \]

9.3.2.12 Improper integrals

1.27 $

30 Problem: Examine the improper integral for convergence: \[ \int_{2}^{3} \frac{\sin 3 x d x}{\sqrt[3]{x^{5}(x-2)}} \]

9.3.2.13 Improper integrals

0.76 $