Solve 3(2x − 1) = 15.
- Divide both sides by 3: 2x − 1 = 5.
- Add 1, then divide by 2: x = 3.
Check: 3(2 × 3 − 1) = 3 × 5 = 15.
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Example · Differentiate the function
f(x) = 3x² − 4x + 7
d/dx [3x²] = 6x
d/dx [−4x] = −4
d/dx [7] = 0
d/dx [−4x] = −4
d/dx [7] = 0
f′(x) = 6x − 4
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A useful solution
The answer is only the last line.
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- Name the method. Identify the rule, formula, theorem, or model that fits the problem.
- Translate the question. Define variables and pull the necessary values, constraints, and units from the prompt.
- Show the transformation. Work through substitutions and algebra in an order you can inspect.
- Check the result. Look for reasonable magnitude, correct units, and agreement with the original conditions.
Worked calculus example
How do you integrate 2x(x² + 1)³?
The expression inside the parentheses has derivative 2x. That is the clue to use substitution instead of expanding the polynomial.
If the question is in an image, use the screenshot homework solver to capture the full expression, including exponents and bounds.
CHECK THE METHOD
- Let u = x² + 1. Then du = 2x dx.
- Rewrite the integral as ∫u³ du.
- Integrate: u⁴/4 + C.
- Substitute back: (x² + 1)⁴/4 + C.
Verify it: Differentiating (x² + 1)⁴/4 gives 2x(x² + 1)³, the original integrand.
More checked examples
A solution should survive a second look.
These examples show how to verify a result after working through the steps. AI-generated answers to new problems can still be wrong.
Find the line through (2, 3) and (4, 7).
- Calculate the slope: (7 − 3) ÷ (4 − 2) = 2.
- Use y − 3 = 2(x − 2), then simplify to y = 2x − 1.
Check: The line gives y = 3 at x = 2 and y = 7 at x = 4.
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What types of math homework can the AI solver help with?
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