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

The integral of (y^3)/(x^4) is (y^4)/(4x^4)+C

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integral of (y^3)/(x^4)

integral

\frac{y ^{3}}{x ^{4}}

\frac{y ^{4}}{4 x ^{4}} + C

Solution steps

\int \frac{y ^{3}}{x ^{4}} d y

Take the constant out:

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

= \frac{1}{x ^{4}} \cdot \int y^{3} d y

Apply the Power Rule

= \frac{1}{x ^{4}} \cdot \frac{y ^{4}}{4}

Simplify

\frac{1}{x ^{4}} \cdot \frac{y ^{4}}{4} : \frac{y ^{4}}{4 x ^{4}}

= \frac{y ^{4}}{4 x ^{4}}

Add a constant to the solution

= \frac{y ^{4}}{4 x ^{4}} + C

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