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Integral of $$$y^{3}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int y^{3}\, dy$$$.
Solution
Apply the power rule $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=3$$$:
$${\color{red}{\int{y^{3} d y}}}={\color{red}{\frac{y^{1 + 3}}{1 + 3}}}={\color{red}{\left(\frac{y^{4}}{4}\right)}}$$
Therefore,
$$\int{y^{3} d y} = \frac{y^{4}}{4}$$
Add the constant of integration:
$$\int{y^{3} d y} = \frac{y^{4}}{4}+C$$
Answer
$$$\int y^{3}\, dy = \frac{y^{4}}{4} + C$$$A
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