What is expand ln((1+x^2)^{cos(x)}) ?

The solution to expand ln((1+x^2)^{cos(x)}) is cos(x)ln(1+x^2)

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expand ln((1+x^2)^{cos(x)})

expand

ln ((1 + x^{2})^{c o s (x)})

cos (x) ln (1 + x^{2})

Solution steps

ln ((1 + x^{2})^{c o s (x)})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((1 + x^{2})^{c o s (x)}) = cos (x) ln (1 + x^{2})

= cos (x) ln (1 + x^{2})

lo g_{3} (x + 2) + lo g_{3} (x) - lo g_{3} (2)

lo g_{3} (a) + lo g_{3} (a + 3)

lo g_{3} (a) + lo g_{3} (a + 4)

lo g_{3} (a) + lo g_{3} (a + 7)

ln (\frac{e}{7})

What is expand ln((1+x^2)^{cos(x)}) ?
The solution to expand ln((1+x^2)^{cos(x)}) is cos(x)ln(1+x^2)