Calculating integrals of a real variable using residues

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Problem: Appropriately applying the Cauchy residue theorem, find the principal value of the integral: \[ \int_{-\infty}^{+\infty} \frac{\cos \lambda x}{1-x^{4}} d x, \lambda \in \mathbb{R} \]

10.7.16 Calculating integrals of a real variable using residues

6.36 $

Problem: Calculate the integral using residues: \[ \int_{0}^{2 \pi} \frac{d t}{7+\sqrt{13} \sin t} \text {. } \]

10.7.17 Calculating integrals of a real variable using residues

0 $

Problem: Calculate the integral using residues: \[ \int_{0}^{2 \pi} \frac{d t}{(5+2 \sqrt{6} \cos t)^{2}} \text {. } \]

10.7.18 Calculating integrals of a real variable using residues

3.05 $

Problem: Calculate the integral using residues: \[ \int_{-\infty}^{\infty} \frac{x^{2}}{\left(x^{2}+4\right)\left(x^{2}+9\right)} d x \text {. } \]

10.7.19 Calculating integrals of a real variable using residues

2.54 $

Problem: Calculate the integral using residues: \[ \int_{-\infty}^{\infty} \frac{1}{x^{2}+4 x+29} d x \text {. } \]

10.7.20 Calculating integrals of a real variable using residues

2.03 $

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