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Calculus/Indefinite integral-Change of Variable

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Question
Find the indefinite integral (X^2 + 1)^3 X^3 dx . Could you please show all the steps to calculate this indefinite integral. I don't understand how to calculate this problem.

Answer
Find the indefinite integral (X^2 + 1)^3 X^3 dx . Could you please show all the steps to calculate this indefinite integral. I don't understand how to calculate this problem.
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Why not just multiply out?

(X^2 + 1)^3 X^3 =

(x^6 + 3x^4 + 3x^2 + 1)x^3

etc.

Calculus

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Paul Klarreich

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All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

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I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

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