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Popular >

integral of x(1+y)

Solution

\int x (1 + y) d y

Solution

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

Solution steps

\int x (1 + y) d y

Take the constant out:

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

= x \cdot \int 1 + 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

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

\int 1 d y = y

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 1/(y+4)

\int \frac{1}{y + 4} d y

integral of ((x))/((7x^2+3)^5)

\int \frac{( x )}{( 7 x ^{2} + 3 ) ^{5}} d x

integral of (1-4t^2)^{3/2}

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

integral of 2xsin^2(x)+2xcos^2(x)integral

2 x sin^{2} (x) + 2 x cos^{2} (x)

integral of (2x+cos(3x))/(3x^2+sin(3x))

\int \frac{2 x + cos ( 3 x )}{3 x ^{2} + sin ( 3 x )} d x

Frequently Asked Questions (FAQ)

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