Integration Techniques and Antiderivatives

This video tutorial provides a comprehensive overview of basic integration formulas useful for Calculus 1 and 2. It covers the integration of constants, power rule, rational functions, exponential functions, logarithmic functions, and trigonometric functions. The video also explains integration by parts and offers examples for better understanding. Additional resources and formula sheets are available in the description.

What is the integral of a constant 'a' with respect to x?

• a + C

• ax + C

• a/x + C

• a^x + C

How do you find the antiderivative of x^n?

• x^(n-1) / (n-1) + C

• x^n / n + C

• nx^(n-1) + C

• x^(n+1) / (n+1) + C

What is the integral of a function raised to a power, (ax + b)^n?

• (ax + b)^(n-1)/(n-1) + C

• 1/a * (ax + b)^(n+1)/(n+1) + C

• (ax + b)^(n+1)/(n+1) + C

• a * (ax + b)^(n+1)/(n+1) + C

What is the antiderivative of 1/x?

• ln(x) + C

• 1/x + C

• xln(x) + C

• x^2/2 + C

How do you integrate a rational function of the form 1/(ax + b)?

• ln(a/x + b) + C

• ln(ax + b) + C

• 1/a * ln(ax + b) + C

• a * ln(ax + b) + C

How do you integrate e^(ax + b)?

• 1/a * e^(ax + b) + C

• e^(ax + b) + C

• ln(e^(ax + b)) + C

• a * e^(ax + b) + C

What is the integral of e^x?

• e^x + C

• 1/e^x + C

• x^e + C

• ln(x) + C

What is the integral of sin(ax + b)?

• cos(ax + b) + C

• -cos(ax + b)/a + C

• sin(ax + b)/a + C

• -sin(ax + b) + C

Which formula is used for integration by parts?

• u'v' - ∫v' du

• uv - ∫v du

• u'v - ∫v du

• uv' - ∫u dv

What is the antiderivative of cos(ax + b)?

• sin(ax + b) + C

• -sin(ax + b)/a + C

• cos(ax + b)/a + C

• -cos(ax + b) + C