What is the integral from 0 to x+y of e^x(y+2z) ?

The integral from 0 to x+y of e^x(y+2z) is e^x(2y^2+3xy+x^2)

Popular >

integral from 0 to x+y of e^x(y+2z)

\int_{0}^{x + y} e^{x} (y + 2 z) d z

e^{x} (2 y^{2} + 3 x y + x^{2})

Solution steps

\int_{0}^{x + y} e^{x} (y + 2 z) d z

Take the constant out:

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

= e^{x} \cdot \int_{0}^{x + y} y + 2 z d z

Apply the Sum Rule:

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

= e^{x} (\int_{0}^{x + y} y d z + \int_{0}^{x + y} 2 z d z)

\int_{0}^{x + y} y d z = y (x + y)

\int_{0}^{x + y} 2 z d z = (x + y)^{2}

= e^{x} (y (x + y) + (x + y)^{2})

Expand

y (x + y) + (x + y)^{2} : 2 y^{2} + 3 x y + x^{2}

= e^{x} (2 y^{2} + 3 x y + x^{2})

\int_{0}^{3} \frac{x - 1}{x + 1} d x

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

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

\int_{0}^{6} 5 d x

\int_{0}^{1} x - \frac{1}{2} d x

What is the integral from 0 to x+y of e^x(y+2z) ?
The integral from 0 to x+y of e^x(y+2z) is e^x(2y^2+3xy+x^2)