Solved example of integral
Expand the integral $\int\left(3x^2+5x+2\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
The integral of a function times a constant ($3$) is equal to the constant times the integral of the function
Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$
Any expression multiplied by $1$ is equal to itself
The integral $\int3x^2dx$ results in: $x^{3}$
The integral of a function times a constant ($5$) is equal to the constant times the integral of the function
Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$
The integral $\int5xdx$ results in: $\frac{5}{2}x^2$
The integral of a constant is equal to the constant times the integral's variable
The integral $\int2dx$ results in: $2x$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
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