What is the integral of (4x^3+2)/(x^2) ?

The integral of (4x^3+2)/(x^2) is -(4x^3+2)/x+6x^2+C

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integral of (4x^3+2)/(x^2)

\int \frac{4 x ^{3} + 2}{x ^{2}} d x

- \frac{4 x ^{3} + 2}{x} + 6 x^{2} + C

Solution steps

\int \frac{4 x ^{3} + 2}{x ^{2}} d x

Apply Integration By Parts

: - \frac{4 x ^{3} + 2}{x} - \int - 12 x d x

= - \frac{4 x ^{3} + 2}{x} - \int - 12 x d x

\int - 12 x d x = - 6 x^{2}

= - \frac{4 x ^{3} + 2}{x} - (- 6 x^{2})

Simplify

= - \frac{4 x ^{3} + 2}{x} + 6 x^{2}

Add a constant to the solution

= - \frac{4 x ^{3} + 2}{x} + 6 x^{2} + C

\frac{d ^{2}}{d x ^{2}} (sin (5 x))

y = cot (1 - 2 x^{2})

x y^{^{'}} + 3 y = \frac{2 e ^{2 x}}{x ^{2}}

\frac{d}{d x} (cos (x) + x^{\frac{5}{4}})

y^{^{''}} - 4 y^{^{'}} - 5 y = 5 x

What is the integral of (4x^3+2)/(x^2) ?
The integral of (4x^3+2)/(x^2) is -(4x^3+2)/x+6x^2+C