How do you integrate $\frac{4 x + 7}{2 x + 5} d x$ $(4x+7)/(2x+5) dx$ ?

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How do you integrate $\frac{4 x + 7}{2 x + 5} d x$ $(4x+7)/(2x+5) dx$ ?

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Answer 1 · 2015-04-21T19:38:45

Simple math ! $\Rightarrow$ $=>$

$\int \frac{4 x + 7}{2 x + 5} d x = 2 \int \frac{4 x + 7}{4 x + 10} d x = 2 \int \frac{4 x + 10 - 3}{4 x + 10} d x$ $int(4x+7)/(2x+5) dx= 2int(4x+7)/(4x+10)dx = 2int(4x+10-3)/(4x+10)dx$

$2 \int 1 d x - 3 \int \frac{1}{4 x + 10} d x = 2 \int 1 d x - \frac{3}{2} \int \frac{2}{2 x + 5} d x$ $2int1dx-3int1/(4x+10) dx= 2int1dx-3/2int2/(2x+5)dx$

$[2 x] - \frac{3}{2} [ln (2 x + 5)] + C$ $[2x]-3/2[ln(2x+5)]+C$

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How do you integrate $\frac{4 x + 7}{2 x + 5} d x$ $(4x+7)/(2x+5) dx$ ?

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