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Solving 4 questions…
Page 1
Q1 $\frac{e^{3x}}{27}(9x^2 - 6x + 2) + C$
1 Let $u=x^2$, $dv=e^{3x}dx$
2 Apply IBP twice to reduce the power of $x$
3 Factor out $e^{3x}/27$
Q2 $2\ln|x| - \frac{1}{2}\ln|x-1| + \frac{3}{2}\ln|x+1| + C$
Q3 $\sqrt{x^2-9} - 3\sec^{-1}(x/3) + C$
Q4 Solving…

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Study Mode
Integration by Parts
When you have a product of two functions where one simplifies when differentiated, use IBP:
$\int u\,dv = uv - \int v\,du$
Tip: Use LIATE to pick $u$: Logs → Inverse trig → Algebraic → Trig → Exponential
Try this
Evaluate $\int x\,\ln x\,dx$ using integration by parts.
72%
Good setup! You correctly identified $u$ and $dv$. Watch the sign when substituting back — that's where the error crept in.

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Solution

Using Newton's second law, $F = ma$:

Given $F = 25\text{ N}$ and $m = 5\text{ kg}$:

$$a = \frac{F}{m} = \frac{25}{5} = 5\ \text{m/s}^2$$

The acceleration is 5 m/s² in the direction of the applied force.

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