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Popular >

integral of (4y^3)

Solution

\int (4 y^{3}) d y

Solution

y^{4} + C

Solution steps

\int 4 y^{3} d y

Take the constant out:

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

= 4 \cdot \int y^{3} d y

Apply the Power Rule

: \frac{y ^{4}}{4}

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

Simplify

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

= y^{4}

Add a constant to the solution

= y^{4} + C

Graph

Popular Examples

integral of tan(3/2 x-1)

\int tan (\frac{3}{2} x - 1) d x

integral of x^2(x^3+7)^5

\int x^{2} (x^{3} + 7)^{5} d x

integral of (10x^4)/(x^{10)-1}

\int \frac{10 x ^{4}}{x ^{10} - 1} d x

\int t^{'} d t

integral of 4sin^2(3x)

\int 4 sin^{2} (3 x) d x

Frequently Asked Questions (FAQ)

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