What is the integral of (bz^2+c/z) ?

The integral of (bz^2+c/z) is cln|z|+(bz^3)/3+C

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integral of (bz^2+c/z)

\int (b z^{2} + \frac{c}{z}) d z

c ln ∣ z ∣ + \frac{b z ^{3}}{3} + C

Solution steps

\int b z^{2} + \frac{c}{z} d z

Apply the Sum Rule:

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

= \int \frac{c}{z} d z + \int b z^{2} d z

\int \frac{c}{z} d z = c ln ∣ z ∣

\int b z^{2} d z = \frac{b z ^{3}}{3}

= c ln ∣ z ∣ + \frac{b z ^{3}}{3}

Add a constant to the solution

= c ln ∣ z ∣ + \frac{b z ^{3}}{3} + C

\frac{d}{d x} ((sin (2 x))^{\frac{c o s ( x )}{x ^{3}}})

cos (3^{x})

\frac{d}{d x} (\frac{1 - 2 x}{x})

\frac{d}{d x} (cos (x) - e^{x})

\int tan^{4} (\frac{x}{2}) sec^{4} (\frac{x}{2}) d x

What is the integral of (bz^2+c/z) ?
The integral of (bz^2+c/z) is cln|z|+(bz^3)/3+C