Find the indefinite integral.

15

x

+1

4

x

dx

Step 1

As the integral15

x

+1

4

x

dx

has a sum as the integrand, we use the Sum Rule for Integration,

f(x) +g(x)dx=f(x)dx+g(x)dx,

which says that we can break up integrals at sums and differences.

Our integral is thus

15

x

+1

4

x

dx=15$$

x

dx+$$

1

4x

dx.

Step 2

The first integral is the product of a function and a constant. To integrate it, we use the Constant Multiple Rule for Integration:

kf(x)dx=kf(x)dx,

which states that we can pull constants out of the integral.

Rewriting the first integral, we have:

15

x

dx+1

4

x

dx=15

15

x

dx+1

4

x

dx.

Step 3

To find the integrals more easily, we rewrite each integrand asxto some fractional power.

15

x

dx+1

4

x

dx=15x

dx+x

dx