Evaluate: `int(sinx)/(sin4x)dx`

Explanation

=`I=int frac{sin x}{sin 4 x} d x`
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I=int frac{sin x}{2 sin 2 x cos 2 x} d x=int frac{cos x}{4 cos x cos 2 x}`
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=int frac{d x}{4(1-sin ^{2} x)(1-2 sin ^{2} x)} d x`
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Put sin x=t Rightarrow cos x d x=d t`
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therefore I=int frac{d t}{4(1-t^{2})(1-2 t^{2})}`
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.=frac{1}{4} int frac{1}{t^{2}-1}-frac{1}{t^{2}-frac{1}{2}}) d t`
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=frac{1}{4}[frac{1}{2} log |frac{t-1}{t+1}|-frac{1}{sqrt{2}} log |frac{t+frac{1}{sqrt{2}} ]}{t-C}|+frac{1}{sqrt{2}} ] `
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