Question

How do you evaluate the integral `intx^3+4x^2+5 dx`?

Answer 1

Because this equation only consists of terms added together, you can integrate them separately and add the results, giving us:

`int x^3 + 4x^2 + 5dx = intx^3dx + int4x^2dx + int5dx`

Each of these terms can be integrated using the Power Rule for integration, which is:

`int x^ndx = x^(n+1)/(n+1) + C`

Plugging our 3 terms into this formula, we have:

`int x^3dx = x^(3+1)/(3+1) = x^4/4`

`int 4x^2dx = (4x^(2+1))/(2+1) = (4x^3)/3`

`int 5dx = int 5x^0dx = (5x^(0+1))/(0+1) = (5x^1)/1 = 5x`

Now we arrive at our final answer by adding these together, remembering to add our constant (`C`) on the end:

`int x^3 + 4x^2 + 5dx = x^4/4 + (4x^3)/3 + 5x + C`