Differentiation and Integration Concepts

The function is divided by its base.

The function is multiplied by its derivative.

The function becomes a logarithmic function.

The function remains unchanged.

A constant factor of 1

A scaling factor of log a

A factor of e

A factor of x

It is subtracted from the integral.

It is added as a constant of integration.

It is multiplied by the integral.

It is ignored.

1/x

log a

1/(x log a)

x log a

Ignore it.

Convert it to a positive index.

Use it as is.

Multiply by a negative constant.

e^f - C

f' e^f + C

e^f + C

f e^f + C

A constant

A variable

A function of x

An exponent

To simplify logarithmic expressions

To change the base of exponential functions

To integrate functions that resemble derivatives

To differentiate functions

e^u + C

u + C

u e^u + C

e^u - C

As constants

As fractions

As exponents

As logarithms