∫ _1^2 5dx5x+3 t=5x+3 dt=5dx x→ 1→ 2 t→ 8→ 13∫ _8^13 1 t dt .log t |_8^13 log 13 log 8 ...

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Product Law

Solve: ∫125d...

Question

Solve:
$\int_{1}^{2} \frac{5 d x}{5 x + 3}$

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Solution

$\int_{1}^{2} \frac{5 d x}{5 x + 3} t = 5 x + 3 ⟹ d t = 5 d x x \to 1 \to 2 t \to 8 \to 13 ⟹ \int_{8}^{13} \frac{1}{t} d t {log t |}_{8}^{13} log 13 - log 8$

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3 \int 1 (2 x + 5) d x

Solve:

$2 x - 3 = \frac{3}{10} (5 x - 12)$ .

\frac{5 x - 3}{12} = 1

\frac{5 x - 3}{12} = 1

2 x - 3 = \frac{3}{10} (5 x - 12)

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