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Popular >

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

Solution

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

Solution

y = arctan (x) + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

If

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

then

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

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

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

y = arctan (x) + c_{1}

Popular Examples

derivative of-2x^{9/8}

\frac{d}{d x} (- 2 x^{\frac{9}{8}})

limit as x approaches 30 of 30

x \to 30 lim (30)

integral from 0 to 1 of 8/(sqrt(x)(x+1))

\int_{0}^{1} \frac{8}{x ( x + 1 )} d x

integral from 0 to infinity of 3^{-x}

\int_{0}^{\infty} 3^{- x} d x

integral of x^2(2x+1)

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

Frequently Asked Questions (FAQ)

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