What is the integral of 3/2 ln|x^3|+1 ?

The integral of 3/2 ln|x^3|+1 is 3/2 xln|x^3|-7/2 x+C

integral of 3/2 ln|x^3|+1

\int \frac{3}{2} ln x^{3} + 1 d x

\frac{3}{2} x ln x^{3} - \frac{7}{2} x + C

Solution steps

\int \frac{3}{2} ln x^{3} + 1 d x

Apply Integration By Parts

= x (\frac{3}{2} ln x^{3} + 1) - \int \frac{9}{2} d x

\int \frac{9}{2} d x = \frac{9}{2} x

= x (\frac{3}{2} ln x^{3} + 1) - \frac{9}{2} x

Simplify

x (\frac{3}{2} ln x^{3} + 1) - \frac{9}{2} x : \frac{3}{2} x ln x^{3} - \frac{7}{2} x

= \frac{3}{2} x ln x^{3} - \frac{7}{2} x

Add a constant to the solution

= \frac{3}{2} x ln x^{3} - \frac{7}{2} x + C

d er i v a t i v e f (x) = \frac{x}{x - 1}

t an g e n t f (x) = 3 - 5 x + 2 x^{2}, (- 9, 210)

(x + y)^{2} d x + (2 x y + x^{2} - 9) d y = 0

x \to \infty lim (\frac{x}{2 x})

\frac{\partial}{\partial x} (\frac{x}{2 + y})

What is the integral of 3/2 ln|x^3|+1 ?
The integral of 3/2 ln|x^3|+1 is 3/2 xln|x^3|-7/2 x+C