How do you find $\int (2 x + \frac{3}{x^{2}}) d x$ $\int ( 2x + \frac { 3} { x ^ { 2} } ) d x$ ?

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How do you find $\int (2 x + \frac{3}{x^{2}}) d x$ $\int ( 2x + \frac { 3} { x ^ { 2} } ) d x$ ?

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Answer 1 · 2017-02-05T21:36:06

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

Explanation:

Since $\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x$ $int f(x)+g(x)dx=intf(x)dx+intg(x)dx$

We can say

$\int (2 x + \frac{3}{x^{2}}) d x = \int 2 x d x + \int \frac{3}{x^{2}} d x$ $int(2x+3/x^2)dx=int2xdx+int3/x^2dx$

Also since $\int c x d x = c \int x d x$ $intcxdx=cintxdx$

we can say

$\int 2 x d x + \frac{3}{x^{2}} d x = 2 \int x d x + 3 \int \frac{1}{x^{2}} d x = 2 (\frac{x^{2}}{2}) - 3 (\frac{1}{x})$ $int2xdx+3/x^2dx=2intxdx+3int1/x^2dx=2(x^2/2)-3(1/x)$

Then

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

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How do you find $\int (2 x + \frac{3}{x^{2}}) d x$ $\int ( 2x + \frac { 3} { x ^ { 2} } ) d x$ ?

1 Answer

Explanation:

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How do you find \int ( 2x + \frac { 3} { x ^ { 2} } ) d x∫(2x+3x2)dx\int ( 2x + \frac { 3} { x ^ { 2} } ) d x?

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How do you find $\int (2 x + \frac{3}{x^{2}}) d x$ $\int ( 2x + \frac { 3} { x ^ { 2} } ) d x$ ?