The integral is .

(a) The substitution .

Consider .

Differentiate on each side.

.

Substitute corresponding values in the integral.

Replace in above expression.

.

(b) The substitution .

Consider .

Differentiate on each side.

.

Substitute corresponding values in the integral.

Replace in above expression.

.

(c)

Consider .

Rewrite the integral.

Trigonometric identity: .

(d)

Consider .

Use integral by parts to find the integral.

Integration by parts formula: .

Assume and .

Integrate to find .

Consider .

Differentiate on each side.

.

Substitute corresponding values in the formula.

(a) .

(b) .

(c) .

(d) .