Indefinite integrals

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3) Problem: Calculate the integral: \[ \int e^{5 x^{2}+3 x+1} d x \]

9.3.1.1 Indefinite integrals

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Problem: Calculate the integral: 1) \( \int \frac{d x}{(x-1)^{2}(x-2)} \), 2) \( \int \cos \frac{x}{2} \cos \frac{x}{3} d x \), 3) \( \int \frac{\sqrt[6]{x}+1}{\sqrt[6]{x^{7}}+\sqrt[4]{x^{5}}} d x \).

9.3.1.2 Indefinite integrals

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es Problem: Calculate the integral: 1) \( \int \frac{5 x+3}{\sqrt{3-x^{2}}} d x \), 2) \( \int x \cos ^{2} x d x \).

9.3.1.3 Indefinite integrals

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Problem: Let's calculate the integral: 1) \( \int \frac{d x}{\sqrt{5-x^{2}}} \), 2) \( \int \frac{x+23}{x^{2}+x-20} d x \), 3) \( \int x e^{-7 x} d x \).

9.3.1.4 Indefinite integrals

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Problem: Find indefinite integrals. Check the results by differentiation. 1) \( \int \frac{\tan x}{\cos ^{2} x} \), 2) \( \int \ln 3 x d x \), 3) \( \int \frac{x-8}{x(x-2)^{2}} d x \).

9.3.1.5 Indefinite integrals

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Problem: Calculate the indefinite integral: \[ \int \frac{x^{4}-3 x^{3}+15 x-25}{(x+2)(x-1)(x-3)} d x \]

9.3.1.6 Indefinite integrals

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Problem: Calculate the indefinite integral: \[ \int \frac{-x^{4}-8 x^{3}-18 x^{2}-13 x-1}{(x+1)^{4}(x+2)} d x \]

9.3.1.7 Indefinite integrals

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30 Problem: Calculate the indefinite integral: \[ \int\left(\cos ^{2} x \sin x+x \sqrt{1+x^{2}}\right) d x \]

9.3.1.8 Indefinite integrals

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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

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

9.3.1.10 Indefinite integrals

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

9.3.1.11 Indefinite integrals

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

9.3.1.12 Indefinite integrals

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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

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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

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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

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