Question

Question #4d270

Answer 1

`int (3x)/(2x^2+9) dx=3/4*ln(2x^2+9)+C`

Explanation:

There is no need to reduction to partial fraction. The numerator has the differential of the denominator.

`int (3x)/(2x^2+9) dx=3/4int (4x)/(2x^2+9) dx`

At this point, we can use the formula `int (du)/u=ln u+C`

`int (3x)/(2x^2+9) dx=3/4*ln(2x^2+9)+C`

God bless....I hope the explanation is useful.

Answer 2

`3/4 log(2x^2 + 9)`

Explanation:

`\int 3x/(2x^2+9) dx = 3/4 \int 4x dx/(2x^2 + 9) = 3/4 \int (d(2x^2 + 9))/(2x^2 + 9) = 3/4 log(2x^2 + 9)`