What is the integral of (3x^2+ln(x)) ?

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

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integral of (3x^2+ln(x))

\int (3 x^{2} + ln (x)) d x

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

Solution steps

\int 3 x^{2} + ln (x) 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 3 x^{2} d x + \int ln (x) d x

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

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

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

Add a constant to the solution

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

5 x + 4

\int \frac{sin ( 2 x )}{2 + cos ( x )} d x

\int_{- 5}^{5} \frac{y}{25 - y ^{2}} d y

x^{3} (2 x - 1)^{7}

x \to 0 lim (x + 2)

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