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vovangra [49]
2 years ago
10

Integral pls i couldnt​

Mathematics
1 answer:
olga nikolaevna [1]2 years ago
5 0

Simplify the integrand:

\dfrac{4x^4 + 3x^2 + 5x}{x^2} = 4x^2 + 3 + \dfrac5x

Now integrate one term at a time.

\displaystyle \int 4x^2 \, dx = \frac43 x^3 + C

\displaystyle \int 3 \, dx = 3x + C

\displaystyle \int \frac5x \, dx = 5 \ln|x| + C

Putting everything together,

\displaystyle \int \frac{4x^4 + 3x^2 + 5x}{x^2} \, dx = \int \left(4x^2 + 3 + \frac5x\right) \, dx = \boxed{\frac43 x^3 + 3x + 5 \ln|x| + C}

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Denote the events as follows:

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