積分フローチャート - Integral Solver Guide

Example

Integrating expressions like 1/(x^2 + 3x + 5)

Scenario

In a scenario where a student encounters a complex fractional expression, the flowchart guides through dividing the polynomial until the numerator's degree is less than the denominator's, and then applying partial fraction decomposition if necessary.

Example

Integrating sin(x)^n or cos(x)^n where n is an integer

Scenario

When faced with integrating powers of sine and cosine functions, the flowchart suggests methods based on whether n is odd or even, including substitution and using trigonometric identities to simplify the integral.

Example

Integrating functions like e^x * sin(x) or log(x)^n

Scenario

For integrals involving exponential and logarithmic functions, the flowchart offers strategies such as integration by parts and substitutions that simplify the integral into a more manageable form for calculation.

Example

Integrating polynomial expressions of various degrees

Scenario

When dealing with polynomial expressions, the flowchart provides a straightforward approach to integrate by summarizing the basic antiderivative forms of polynomials, making it easier for students to apply the power rule of integration.

Example

Integrating expressions that lead to inverse trigonometric functions such as arcsin(x), arctan(x)

Scenario

In cases where integration leads to inverse trigonometric functions, the flowchart outlines the conditions under which to use specific substitutions to arrive at the inverse trigonometric form.