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Popular >

integral of (xy+z)

Solution

\int (x y + z) d z

Solution

\frac{z ^{2}}{2} + x yz + C

Solution steps

\int x y + 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

= \int z d z + \int x y d z

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

\int x y d z = x yz

= \frac{z ^{2}}{2} + x yz

Add a constant to the solution

= \frac{z ^{2}}{2} + x yz + C

Popular Examples

integral of x*sin^3(3x)

\int x \cdot sin^{3} (3 x) d x

integral of (4x^2+4x+4)/((x^2+1)^2)

\int \frac{4 x ^{2} + 4 x + 4}{( x ^{2} + 1 ) ^{2}} d x

integral of (9t^2-2)/(3t+1)

\int \frac{9 t ^{2} - 2}{3 t + 1} d t

integral of x/((x-1)(x^2+6x+11))

\int \frac{x}{( x - 1 ) ( x ^{2} + 6 x + 11 )} d x

integral of y^3sqrt(1+y)

\int y^{3} 1 + y d y

Frequently Asked Questions (FAQ)

What is the integral of (xy+z) ?
The integral of (xy+z) is (z^2)/2+xyz+C