Evaluate: `int(cos2x-cos2alpha)/(cosx-cosalpha)\ dx`

Explanation

Solution:

=`\int \frac{(2 \cdot \cos ^{2} x-1)-(2 \cdot \cos ^{2} \alpha-1)}{\cos x-\cos \alpha} \cdot d x(u {sing} \cos 2 \theta=2 \cdot \cos ^{2} \theta-1)`

=`\int \frac{2 \cos ^{2} x-1-2 \cdot \cos ^{2} \alpha+1}{\cos x-\cos \alpha} d x `

=`\int \frac{2 \cos ^{2} x-2 \cos ^{2} \alpha-1+1}{\cos x-\cos \alpha} \cdot d x `

=`\int \frac{2(\cos ^{2} x-\cos 2 \alpha)}{\cos ^{2} x-\cos \alpha} \cdot dx`

=`2 \int \frac{.\int \cos _{x}+\int \cos \alpha \cdot d c]}{\cos ^{2} x-\cos \alpha} \cdot d x `

=`2 \int \frac{(\cos ^{2} x+\cos \alpha) \cdot d x}{\cos ^{2} x \cdot d x+\cos \alpha \int 1} \cdot d x`

=`2 \int \frac{(\cos ^{2} x+\cos \alpha)(\cos x-\cos \alpha)}{(\cos x-\cos \alpha)} \cdot d x`

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