What is the integral of (12)/((1+x+y)^5) ?

The integral of (12)/((1+x+y)^5) is -3/((1+x+y)^4)+C

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integral of (12)/((1+x+y)^5)

\int \frac{12}{( 1 + x + y ) ^{5}} d y

- \frac{3}{( 1 + x + y ) ^{4}} + C

Solution steps

\int \frac{12}{( 1 + x + y ) ^{5}} d y

Take the constant out:

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

= 12 \cdot \int \frac{1}{( 1 + x + y ) ^{5}} d y

Apply u-substitution

= 12 \cdot \int \frac{1}{u ^{5}} d u

Apply the Power Rule

= 12 (- \frac{1}{4 u ^{4}})

Substitute back

u = 1 + x + y

= 12 (- \frac{1}{4 ( 1 + x + y ) ^{4}})

Simplify

12 (- \frac{1}{4 ( 1 + x + y ) ^{4}}) : - \frac{3}{( 1 + x + y ) ^{4}}

= - \frac{3}{( 1 + x + y ) ^{4}}

Add a constant to the solution

= - \frac{3}{( 1 + x + y ) ^{4}} + C

What is the integral of (12)/((1+x+y)^5) ?
The integral of (12)/((1+x+y)^5) is -3/((1+x+y)^4)+C