Mathematic Instruction Media

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Mathematic Instruction Media

Belajar Integral Yuk!!!!

Berapa nilai berikut:
$\int \frac{dx}{1+sin 2x} = ...$
Jawab:
$\begin{eqnarray}\int \frac{dx}{1+\sin 2x}&=&\int \frac{dx}{\sin ^2x+\cos ^2x+2\sin x\cos x}\\&=&\int \frac{dx}{(\sin x+\cos x)^2}\\&=&\int \frac12 \sec ^2\(x-\frac{\pi}4\)\,dx\\&=&\frac12 \tan \(x-\frac{\pi}4\)+C\end{eqnarray}$

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