What is the integral from 4 to 8 of x/(sqrt(x^2-25)) ?

The integral from 4 to 8 of x/(sqrt(x^2-25)) is -3i+sqrt(39)

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integral from 4 to 8 of x/(sqrt(x^2-25))

\int_{4}^{8} \frac{x}{x ^{2} - 25} d x

- 3 i + 39

Solution steps

\int_{4}^{8} \frac{x}{x ^{2} - 25} d x

Adjust integral based on undefined pointsThere is an undefined point within the boundaries at

: 5

= \int_{4}^{5} \frac{x}{x ^{2} - 25} d x + \int_{5}^{8} \frac{x}{x ^{2} - 25} d x

\int_{4}^{5} \frac{x}{x ^{2} - 25} d x = - 3 i

= - 3 i + \int_{5}^{8} \frac{x}{x ^{2} - 25} d x

\int_{5}^{8} \frac{x}{x ^{2} - 25} d x = 39

= - 3 i + 39

What is the integral from 4 to 8 of x/(sqrt(x^2-25)) ?
The integral from 4 to 8 of x/(sqrt(x^2-25)) is -3i+sqrt(39)