Integration By Substitution Calculator
Work out integration by substitution instantly with clear inputs, formula shown and shareable results.
About Integration By Substitution Calculator
Substitution reverses the chain rule. Setting u = ax + b gives du = a dx, so ∫(ax + b)ᵖ dx becomes (1/a)∫uᵖ du = (ax + b)^(p+1) / (a(p + 1)) + C.
Formula
Linear substitution
∫(ax + b)ᵖ dx = (ax + b)^(p+1) / (a(p + 1)) + C
Worked example
With the default values below, Integration By Substitution Calculator returns Definite integral from 0 to your limit of 288.20000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Inner function a·x + b: coefficient a
- 2
- Constant b
- 3
- Outer power p in (ax + b)ᵖ
- 4
- Evaluate the integral from 0 to
- 1
Results
- Definite integral from 0 to your limit
- 288.20000000
- Substitution used
- u = 2x + 3, du = 2 dx
- u at the upper limit
- 5.000000
- u at the lower limit
- 3.000000
Step by step
- 1Values used
- 2Linear substitution
- 3Definite integral from 0 to your limit= 288.20000000
- 4Substitution used= u = 2x + 3, du = 2 dx
- 5u at the upper limit= 5.000000
- 6u at the lower limit= 3.000000
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Integrate (2x + 3)⁴ from 0 to 1.
(2x+3)⁵/10 evaluated gives (3125 − 243)/10 = 288.2.
Must I change the limits?
Only if you leave the answer in terms of u. Converting back to x lets you use the original limits.