Please solve int(3x^5-2/x^3)dx?

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Please solve int(3x^5-2/x^3)dx?

$\int (3 x^{5} - \frac{2}{x^{3}}) d x$ $int(3x^5-2/x^3)dx$

1 Answer

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Answer 1 · 2018-04-12T08:08:03

$I = \frac{1}{2} x^{6} + x^{- 2} + C$ $I=1/2x^(6)+x^(-2)+C$

Explanation:

We want to integrate

$I = \int 3 x^{5} - \frac{2}{x^{3}} d x = 3 \int x^{5} d x - 2 \int x^{- 3} d x$ $I=int3x^5-2/x^3dx=3intx^5dx-2intx^-3dx$

Remember the power rule for integration

$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C$ $color(blue)(intx^ndx=(x^(n+1))/(n+1)+C$

Thus, by the power rule

$I = \frac{3 x^{5 + 1}}{5 + 1} - \frac{2 x^{- 3 + 1}}{- 3 + 1} + C$ $I=(3x^(5+1))/(5+1)-(2x^(-3+1))/(-3+1)+C$

$I = \frac{3 x^{6}}{6} - \frac{2 x^{- 2}}{- 2} + C$ $color(white)(I)=(3x^(6))/(6)-(2x^(-2))/(-2)+C$

$I = \frac{1}{2} x^{6} + x^{- 2} + C$ $color(white)(I)=1/2x^(6)+x^(-2)+C$

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Please solve int(3x^5-2/x^3)dx?

$\int (3 x^{5} - \frac{2}{x^{3}}) d x$ $int(3x^5-2/x^3)dx$

1 Answer

Explanation:

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Please solve int(3x^5-2/x^3)dx?

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1 Answer

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$\int (3 x^{5} - \frac{2}{x^{3}}) d x$ $int(3x^5-2/x^3)dx$