 | (x2 - 3x-1 + 4) | dx |
Look at the given expression,
| (x2 - 3x-1 + 4) | dx |
The first rule to remember is this: constant coefficients such as the 3 in front of the x-1 always "go along for the ride." In other words, we can just copy them over when taking the antiderivative (see below).
 | x2 dx | = |  3 | + C. |
Now look at the second term.
| 3x-1 | dx. |
Since the 3 "goes along for the ride, we can write
| 3x-1 | dx | = | 3 | x-1 dx. | = | 3 ln|x| + C | Using the special case of the power rule. |
That takes care of the second term. The third term is
| 4 dx | = | 4x + C. | See the table of examples in the tutorial |
Putting them all together gives:
| (x2 - 3x-1 + 4) | dx | = | 3 |
- 3ln|x| + 4x + C. |
You can enter this as x^3/3 - 3ln(abs(x)) + 4x + C
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