What is expand (ln(x^2)sin^3(x))/(sqrt(x^2+1)) ?

The solution to expand (ln(x^2)sin^3(x))/(sqrt(x^2+1)) is (2sin^3(x)ln(x)sqrt(x^2+1))/(x^2+1)

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expand (ln(x^2)sin^3(x))/(sqrt(x^2+1))

expand

\frac{ln ( x ^{2} ) sin ^{3} ( x )}{x ^{2} + 1}

\frac{2 sin ^{3} ( x ) ln ( x ) x ^{2} + 1}{x ^{2} + 1}

Solution steps

\frac{ln ( x ^{2} ) sin ^{3} ( x )}{x ^{2} + 1}

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= \frac{2 ln ( x ) sin ^{3} ( x )}{x ^{2} + 1}

Multiply by the conjugate

\frac{x ^{2} + 1}{x ^{2} + 1}

= \frac{2 ln ( x ) sin ^{3} ( x ) x ^{2} + 1}{x ^{2} + 1 x ^{2} + 1}

x^{2} + 1 x^{2} + 1 = x^{2} + 1

= \frac{2 sin ^{3} ( x ) ln ( x ) x ^{2} + 1}{x ^{2} + 1}

ln (a + a^{2} + 4) - C ln (a + 2) - ln (2) + C ln (2)

ln (1 \cdot 1 0^{7})

2 lo g_{6} (z) - \frac{1}{4} lo g_{6} (w) + 6 lo g_{6} (y)

- 3 ln (2) + ln (3)

lo g_{2} (x^{9})

What is expand (ln(x^2)sin^3(x))/(sqrt(x^2+1)) ?
The solution to expand (ln(x^2)sin^3(x))/(sqrt(x^2+1)) is (2sin^3(x)ln(x)sqrt(x^2+1))/(x^2+1)