Practice u-Substitution in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An integration technique where you substitute u = g(x) and du = g'(x)\,dx to transform a complicated integral into a simpler one. It is the reverse of the chain rule for differentiation.
When you see a composite function inside an integral along with its inner derivative lurking nearby, substitution collapses the composition into a single variable. It's like un-nesting a function: replace the inner part with u, and the integral becomes simpler.
Example 1
easyFind \displaystyle\int 3x^2(x^3+1)^4\,dx.
Example 2
mediumEvaluate \displaystyle\int_0^1 xe^{x^2}\,dx.
Example 3
easyFind \displaystyle\int \cos(5x)\,dx.
Example 4
hardFind \displaystyle\int \frac{\ln x}{x}\,dx.