Integration Techniques and Concepts

Sine inverse has a square root, cosine inverse does not.

Cosine inverse has a square root, sine inverse does not.

Cosine inverse is negative, sine inverse is positive.

Sine inverse is positive, cosine inverse is negative.

Identify the product of functions.

Integrate both functions.

Select u and dv.

Differentiate both functions.

The sum of two integrals.

The integration of a single function.

The product of two functions.

The integration by parts formula.

Choose functions that are identical.

Pick functions that are unrelated.

Select functions that are difficult to differentiate.

Choose functions that are easy to differentiate and integrate.

To simplify the differentiation process.

To eliminate constants.

To transform the integral into a simpler form.

To complicate the integral.

w = 1 - x^2

t = x + 1

u = x^2

v = x

w to the power of two

w to the power of minus three halves

w to the power of zero

w to the power of one half

x sine inverse minus the square root of w

x tangent inverse minus the square root of w

x sine inverse plus the square root of w

x cosine inverse plus the square root of w

It simplifies complex integrals.

It complicates simple integrals.

It eliminates the need for substitution.

It only works for polynomial functions.

It is only useful for trigonometric functions.

It is a magical tool for simplifying integrals.

It is only applicable to definite integrals.

It is rarely used in calculus.