What is the integral of (x^2)/u ?

The integral of (x^2)/u is x^2ln|u|+C

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integral of (x^2)/u

\int \frac{x ^{2}}{u} d u

x^{2} ln ∣ u ∣ + C

Solution steps

\int \frac{x ^{2}}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x^{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= x^{2} ln ∣ u ∣

Add a constant to the solution

= x^{2} ln ∣ u ∣ + C

f (x) = x^{2} arctan (4 x)

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

h (x) = \frac{7}{x ^{2}}

\frac{( s + 1 )}{( s \cdot ( s ^{2} + s + 1 ) )}

n = 5 \sum \infty \frac{1}{2 ^{2 n}}