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Home / Calculate the integral \( \int (4x^3 - 2x + 1) \, dx \).

Calculate the integral \( \int (4x^3 - 2x + 1) \, dx \).

February 22, 2026

$Calculate the integral \( \int (4x^3 - 2x + 1) \, dx \).$

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Use the Pythagorean theorem: \( a^2 + b^2 = c^2 \) for a right triangle.
Check: \( 7^2 + 24^2 = 49 + 576 = 625 \).
Also, \( 25^2 = 625 \).
Integrate each term:
\( \int 4x^3 \, dx = x^4 \),
Combine and add the constant of integration \( C \):

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