U-Substitution

Front

What is U-Substitution in calculus?

Back

U-Substitution is a method used to simplify the integration process by substituting a part of the integrand with a new variable (u), making the integral easier to solve.

Front

When should you use U-Substitution?

Back

Use U-Substitution when the integrand is a composite function or when a function and its derivative appear in the integral.

Front

What is the formula for U-Substitution?

Back

If u = g(x), then du = g'(x)dx. The integral becomes ∫f(g(x))g'(x)dx = ∫f(u)du.

Front

How do you choose u in U-Substitution?

Back

Choose u to be a function inside another function or a part of the integrand that simplifies the integral when substituted.

Front

What is the integral of sec(x)tan(x) dx?

Back

sec(x) + C.

Front

What is the integral of x(x^2 + 7)^(1/3) dx?

Back

(3/8)(x^2 + 7)^(4/3) + C.

Front

What is the integral of (3x^4 + 2)^4(12x^3) dx?

Back

(1/5)(3x^4 + 2)^5 + C.

Front

What is the integral of (2 - x)^5 dx?

Back

-(1/6)(2 - x)^6 + C.

Front

What is the integral of 2x cos(x^2) dx?

Back

sin(x^2) + C.

Front

What is the derivative of u = g(x)?

Back

The derivative of u with respect to x is g'(x).