Answer to Question #108097 in Calculus for Nimra

Question

∫(x² + 4xy) dx

Answer 1

$\int (x^2 + 4xy) \, dx$

$= \int x^2 \, dx + \int 4xy \, dx \hspace{1 cm}$ [ $\because \int (f(x) + g(x)) \, dx = \int f(x) \, dx + \int g(x) \, dx \,\,$ ( Where $f(x) \text{ and } g(x)$ both are functions ) ]

$= \int x^2 \, dx + 4y \int x \, dx \hspace{1 cm}$ [ $\because \int cf(x) \, dx = c \int f(x) \, dx \,\,$ ( Where $c$ is a constant and $f(x)$ is a function ) ]

$= \frac{x^3}{3} + 2yx^2 + C \hspace{1 cm}$ [ $\because \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \,\,$ ( Where $C$ is a constant of integration) ]