### SOLUTIONS TO INTEGRATION USING A POWER SUBSTITUTION

SOLUTION 1 : Integrate . Use the power substitution

so that

and

.

Substitute into the original problem, replacing all forms of , getting

(Use polynomial division.)

.

SOLUTION 2 : Integrate . Use the power substitution

so that

and

.

Substitute into the original problem, replacing all forms of , getting

(Use polynomial division.)

.

SOLUTION 3 : Integrate . Use the power substitution

so that

and

.

Substitute into the original problem, replacing all forms of , getting

(Use polynomial division.)

.

SOLUTION 4 : Integrate . Use the power substitution

so that

,

,

and

.

Substitute into the original problem, replacing all forms of , getting

.

SOLUTION 5 : Integrate . Use the power substitution

so that

,

,

and

.

Substitute into the original problem, replacing all forms of , getting

.

SOLUTION 6 : Integrate . Use the power substitution

so that

,

,

and

.

Substitute into the original problem, replacing all forms of , getting

(Use polynomial division.)

.

Duane Kouba 2000-05-09