### Questions (74)

 7 Sigma notation for sum of $\ln(x)^2$ from $2$ to $20$ with steps of $0.5$ 5 Evaluate $\sum_{r=2}^{\infty} \frac{2-r}{r(r+1)(r+2)}$ 5 Integral of $\int\frac{\sin x}{\sin x+\cos x}dx$ 4 Sum of two infinite complex geometric sums 3 the roots of the equation $ax^2 +bx+c=0$ are $\alpha$ and $\beta$ find an equation with roots $\alpha + \beta$ and $\alpha \beta$.

### Reputation (539)

 +5 By creating a Maclaurin series up to an including $x^4$ for $\ln(\cos x)$ shows that $\ln2 \approx \frac{\pi^2}{16}\left( 1+\frac{\pi^2}{96}\right)$ +5 Evaluate the following integral using the substitution $x=9\sinh^2\theta$ $\int_0^1\sqrt{\frac{x+9}{x}}dx$ +2 find the curve of best fit of the type $y= a \sin(bx)$ by the method of least squares +5 Evaluate the two integrals by considering $C+iS$ $C=\int_0^{\pi/2} e^{2x}\cos 3x dx \qquad S=\int_0^{\pi/2}e^{2x}\sin3xdx$

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