Rewrite as plus

Rewrite as .

Using the Pythagorean Identity, rewrite as .

Let . Find .

Differentiate .

The derivative of with respect to is .

Substitute the lower limit in for in .

The exact value of is .

Substitute the upper limit in for in .

The exact value of is .

The values found for and will be used to evaluate the definite integral.

Rewrite the problem using , , and the new limits of integration.

Apply the distributive property.

Reorder and .

Multiply by .

Use the power rule to combine exponents.

Add and .

Reorder and .

Split the single integral into multiple integrals.

By the Power Rule, the integral of with respect to is .

By the Power Rule, the integral of with respect to is .

Combine and .

Evaluate at and at .

Simplify.

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Raise to the power of .

Combine and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Raise to the power of .

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Raising to any positive power yields .

Multiply by .

Raising to any positive power yields .

Multiply by .

Add and .

Multiply by .

Add and .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form:

Evaluate integral from 0 to pi/3 of tan(x)^5sec(x)^4 with respect to x