Integration Techniques and Trigonometric Identities

The integral involves exponential functions.

The integral is indefinite.

The integral involves a product of sine and cosine functions.

The integral involves a polynomial function.

Sine double angle identity

Tangent identity

Cosine double angle identity

Pythagorean identity

By using the Pythagorean identity

By using the tangent identity

By using the sine double angle identity

By expressing it in terms of cosine

To make the integral more complex

To eliminate trigonometric functions

To simplify the integration process

To change the limits of integration

Tangent identity

Pythagorean identity

Sine double angle identity

Cosine double angle identity

1

x

x^2

0

-1/4 sin(4x)

-cos(4x)

4x

sin(4x)

Because the limits are zero

Because the integral is indefinite

Because substitutions were made

Because only trigonometric identities were used

1

1/2

√3/2

0

π/48 - √3/64

π/6

√3/2

0