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Popular >

integral of (1+xy)

Solution

\int (1 + x y) d y

Solution

y + \frac{x y ^{2}}{2} + C

Solution steps

\int 1 + x y d y

Apply the Sum Rule:

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

= \int 1 d y + \int x y d y

\int 1 d y = y

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

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

Add a constant to the solution

= y + \frac{x y ^{2}}{2} + C

Popular Examples

sum from n=0 to infinity of 1/(3n+1)

n = 0 \sum \infty \frac{1}{3 n + 1}

(\frac{2}{x})^{^{'}}

integral from-1 to 1 of 1/2 x^2

\int_{- 1}^{1} \frac{1}{2} x^{2} d x

(dy)/(dx)=y(y^2-1)

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

derivative of y=x^2+2x-4 derivative of

y = x^{2} + 2 x - 4

Frequently Asked Questions (FAQ)

What is the integral of (1+xy) ?
The integral of (1+xy) is y+(xy^2)/2+C