What is the integral of ln|x|sin(x) ?

The integral of ln|x|sin(x) is -ln|x|cos(x)+\Ci(x)+C

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integral of ln|x|sin(x)

\int ln ∣ x ∣ sin (x) d x

- ln ∣ x ∣ cos (x) + Ci (x) + C

Solution steps

\int ln ∣ x ∣ sin (x) d x

Apply Integration By Parts

: - ln ∣ x ∣ cos (x) - \int - \frac{cos ( x )}{x} d x

= - ln ∣ x ∣ cos (x) - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - ln ∣ x ∣ cos (x) - (- Ci (x))

Simplify

= - ln ∣ x ∣ cos (x) + Ci (x)

Add a constant to the solution

= - ln ∣ x ∣ cos (x) + Ci (x) + C

9 x^{3} (x^{2} - 2)

f (x) = \frac{( x + 1 ) ^{2}}{3 x - 4}

\int \frac{3 - 18 x}{4 - 9 x ^{2}} d x

\int \frac{1}{( 1 - 6 x ) ^{4}} d x

\frac{( s + 1 )}{( s ^{2} + s + 1 )}

What is the integral of ln|x|sin(x) ?
The integral of ln|x|sin(x) is -ln|x|cos(x)+\Ci(x)+C