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Popular >

integral of 4y^3x

Solution

\int 4 y^{3} x d y

Solution

x y^{4} + C

Solution steps

\int 4 y^{3} x d y

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

= x y^{4}

Add a constant to the solution

= x y^{4} + C

Popular Examples

integral of (a^2-x^2)/2

\int \frac{a ^{2} - x ^{2}}{2} d x

derivative of f(x)=(x+1810)/(70(x+2))derivative of

f (x) = \frac{x + 1810}{70 ( x + 2 )}

integral of sqrt(x^2-6x+13)

\int x^{2} - 6 x + 13 d x

x^2(dy)/(dx)-2xy=4y^4

x^{2} \frac{d y}{d x} - 2 x y = 4 y^{4}

integral of t^2e^{-11t}

\int t^{2} e^{- 11 t} d t

Frequently Asked Questions (FAQ)

What is the integral of 4y^3x ?
The integral of 4y^3x is xy^4+C