perplexus.info :: Just Math : Back to basics

Back to basics (Posted on 2021-12-23)

Evaluate:
∫[(5x⁴)*(x⁵-17)]dx.

Explain your method.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Two ways plus a constant

| Comment 1 of 4

This seems a bit trivial for a perplexus problem but I'll give it a go.

Since this is just a polynomial we can just write it in standard form and integrate directly:

∫[(5x⁴)*(x⁵-17)]dx

∫(5x⁹-85x⁴)dx

.5x¹⁰-17x⁵+C

It is obvious, though, that the creator of this problem had u substitution in mind.

Let u = x⁵-17

du = (5x⁴)dx

∫[(x⁵-17)]du

∫[u]du

.5(u²)+C

.5(x⁵-17)²+C

.5x¹⁰-17x⁵+289/2+C

The solutions look slightly different because the 289/2 can be part of the C.

Posted by Jer on 2021-12-23 09:21:16

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