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Katena32 [7]
2 years ago
10

HELP PLEASE

Mathematics
1 answer:
Westkost [7]2 years ago
8 0

Answer:

So in other words, each week he works, he gets an additional $10, to add to his collection of really $75.

Step-by-step explanation:

so, he has $85 in savings, and that he has the opportunity to gain allowance by the following function of 10(x-1).  

total funds(x) = 85 + 10(x-1)  

T(x) = 85 + 10x - 10  

T(x) = 10x + 75

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\displaystyle \int x^3 \ln(x)^2 \, dx

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\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du

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\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)

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\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C

\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C

\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}

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