5
votes
2answers
182 views

Absolute values in $\int \frac{dx}{(x+2)\sqrt{(x+1)(x+3)}}$

in my math class we were given a list of indefinite integrals, and one of them was: $$\int \frac{dx}{(x+2)\sqrt{(x+1)(x+3)}}$$ My working: $$\int \frac{dx}{(x+2)\sqrt{(x+1)(x+3)}}=\int ...
3
votes
6answers
328 views

Evaluating $\int |x|^3 \; dx $

$$\int |x|^3 \; dx $$ In my module it is suggest to use integration by parts, $$ \text{ Set }I = \int (|x|^3 \cdot 1) \; dx = |x|^3 \cdot x - \int \color{red}{\frac {x^3}{|x|^3}3x^2}\cdot x \; dx$$ ...