U-Substitution and Integrals Concepts

The derivative of the function

The outermost function

The function with the highest power

The innermost function

x^2 - 8x

x^2 - 8

2x

x^2 + 8

2x dx

dx

x dx

2 dx

x^2 + 8x - 1

x^2 - 8x + 1

x^2 - 8

x^2 + 1

dx

2x dx

2x + 8 dx

2x - 8 dx

Use the entire expression as U

Use the expression inside the radical as U

Use the square root as U

Ignore them

U^(1/2) + C

3/2 U^(2/3) + C

1/2 U^(3/2) + C

2/3 U^(3/2) + C

The angle

The entire function

The constant

The derivative of the function

Cosecant U

Tangent U

Cosine U

Sine U

The entire expression

The base

The derivative

The exponent