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Popular >

integral of 6xy^3

Solution

\int 6 x y^{3} d x

Solution

3 y^{3} x^{2} + C

Solution steps

\int 6 x y^{3} d x

Take the constant out:

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

= 6 y^{3} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 6 y^{3} \frac{x ^{2}}{2}

Simplify

6 y^{3} \frac{x ^{2}}{2} : 3 y^{3} x^{2}

= 3 y^{3} x^{2}

Add a constant to the solution

= 3 y^{3} x^{2} + C

Popular Examples

implicit (dy)/(dx),3x^3+9xy^2=5x^3 implicit derivative

\frac{d y}{d x}, 3 x^{3} + 9 x y^{2} = 5 x^{3}

derivative of (x^2+3x+2/(x+1))

\frac{d}{d x} (\frac{x ^{2} + 3 x + 2}{x + 1})

inverse oflaplace 9/((s-2)(s-3))inverse laplace

\frac{9}{( s - 2 ) ( s - 3 )}

derivative of f(x)=(2x)(4x^2+6x^7+8)derivative of

f (x) = (2 x) (4 x^{2} + 6 x^{7} + 8)

integral of 1/(sqrt(b^2+a^2x^2))

\int \frac{1}{b ^{2} + a ^{2} x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of 6xy^3 ?
The integral of 6xy^3 is 3y^3x^2+C