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Problem: Calculate the indefinite integral: \[ \int(x \ln (1+x)-x \cos x) d x \]

9.3.1.9 Indefinite integrals

0.75 $

3 Problem: Calculate the indefinite integral: \[ \int \frac{d x}{x^{3}-2 x^{2}+x} \]

9.3.1.10 Indefinite integrals

0.75 $

(3) Problem: Calculate the indefinite integral: \[ \int \frac{d x}{(x-1) \sqrt[4]{x^{3}}} \]

9.3.1.11 Indefinite integrals

0.75 $

(3) Problem: Calculate the indefinite integral: \[ \int \frac{2 x-8}{\sqrt{1-x-x^{2}}} d x \]

9.3.1.12 Indefinite integrals

0.75 $

3) Problem: Calculate the indefinite integral: \[ \int\left(\frac{\sin ^{5} x}{\cos ^{3} x}-\cot ^{4} x\right) d x \]

9.3.1.13 Indefinite integrals

1.5 $

Problem: Calculate the indefinite inetrgal: \[ \int \frac{2 x+3}{\sqrt[4]{x^{2}+3 x+1}} d x \]

9.3.1.14 Indefinite integrals

0 $

Problem: Calculate the indefinite integral: \[ \int \frac{x+4}{\left(x^{2}+2 x+4\right) \sqrt{x^{2}+2 x+5}} d x . \]

9.3.1.15 Indefinite integrals

1.75 $

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

9.3.2.6 Improper integrals

0 $

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

1.25 $

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

0 $

(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

0 $

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

2.5 $

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

9.3.2.11 Improper integrals

0 $

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

9.3.2.12 Improper integrals

1.25 $

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

0.75 $

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