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Popular >

(dy)/(dx)=(x+1)^2

Solution

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

Solution

y = \frac{x ^{3}}{3} + x^{2} + x + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (x + 1)^{2}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int (x + 1)^{2} d x

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

y = \frac{x ^{3}}{3} + x^{2} + x + c_{1}

Popular Examples

integral from 1 to 3 of (x+2)(x-1)^5

\int_{1}^{3} (x + 2) (x - 1)^{5} d x

derivative of (-x^2-4x-1/(4x-3))

\frac{d}{d x} (\frac{- x ^{2} - 4 x - 1}{4 x - 3})

integral of e^{x^3+1}x^2

\int e^{x^{3} + 1} x^{2} d x

derivative of sqrt(ln(e^{3x)+e^{-3x}})

\frac{d}{d x} (ln (e^{3 x} + e^{- 3 x}))

derivative of ln((x+3)/(sqrt(x-1)))derivative of

ln (\frac{x + 3}{x - 1})

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=(x+1)^2 ?
The solution for (dy)/(dx)=(x+1)^2 is y=(x^3)/3+x^2+x+c_{1}