What is the integral of ln(x)-9x^2 ?

The integral of ln(x)-9x^2 is xln(x)-x-3x^3+C

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integral of ln(x)-9x^2

\int ln (x) - 9 x^{2} d x

x ln (x) - x - 3 x^{3} + C

Solution steps

\int ln (x) - 9 x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (x) d x - \int 9 x^{2} d x

\int ln (x) d x = x ln (x) - x

\int 9 x^{2} d x = 3 x^{3}

= x ln (x) - x - 3 x^{3}

Add a constant to the solution

= x ln (x) - x - 3 x^{3} + C

3 sin^{2} (t)

\frac{\partial}{\partial x} (y^{2} + 6 x - x^{2} y + 36)

\int 2 t d t

\int (4 x + 4) 2 x^{2} + 4 x d x

\int 50 x d x

What is the integral of ln(x)-9x^2 ?
The integral of ln(x)-9x^2 is xln(x)-x-3x^3+C