Symbolic Integral Calculator

Enter expressions and coefficients to derive antiderivatives. Export clean results and inspect stepwise rule explanations. Build calculus confidence through consistent pattern-based symbolic practice daily.

Calculator Input

Supported patterns: x^n sin(a*x) cos(a*x) exp(a*x) 1/x 1/(a*x+b) constants

Example Data Table

Input Expression	Integrated Result	Main Rule
5*x^3	1.25x^4 + C	Power rule
cos(3*x)	(1/3)sin(3x) + C	Trig rule
1/(4*x+7)	(1/4)ln\|4x+7\| + C	Substitution rule
2*x+1/x	x^2 + ln\|x\| + C	Linearity + log rule

Formula Used

This calculator applies linearity of integration and a focused library of standard antiderivative rules. Each supported term is integrated separately, then combined into one final expression.

Power rule: ∫xⁿ dx = xⁿ⁺¹ / (n+1), for n ≠ -1
Constant rule: ∫k dx = kx
Log rule: ∫(1/x) dx = ln|x|
Trig rules: ∫sin(ax) dx = -cos(ax)/a, and ∫cos(ax) dx = sin(ax)/a
Exponential rule: ∫exp(ax) dx = exp(ax)/a
Linear denominator rule: ∫1/(ax+b) dx = ln|ax+b|/a

How to Use This Calculator

Type a supported expression such as 3*x^2+sin(2*x)+1/x.
Set the integration variable as a single letter, usually x.
Click Submit to calculate the symbolic antiderivative.
Review the result box shown above the form.
Use the step table to confirm which rule was applied.
Export the finished output with the CSV or PDF buttons.

Supported Input Notes

Use explicit multiplication
Write 3*x^2, not 3x^2.

Combine with plus or minus
Examples: x^2+1/x-cos(4*x).

Stay within supported patterns
This page is educational, not a full CAS engine.

FAQs

1. What does this symbolic integral calculator solve?

It solves common antiderivatives built from supported patterns, including powers, constants, basic trigonometric forms, exponentials, reciprocal terms, and simple linear denominators.

2. Does it work like a full computer algebra system?

No. It is an advanced educational calculator with a targeted rule engine. It focuses on clean, common symbolic forms rather than every possible integral.

3. Why is there a constant of integration?

Indefinite integrals represent entire families of antiderivatives. Any constant disappears during differentiation, so the result must include + C.

4. Can I enter products like x*sin(x)?

Not in this version. Product-rule style integrals usually require integration by parts or deeper symbolic logic beyond the current supported pattern set.

5. How should I type trigonometric expressions?

Use formats such as sin(2*x) or cos(5*x). Keep multiplication explicit and include parentheses around the angle expression.

6. What happens if I enter an unsupported term?

The calculator shows a warning and identifies the unsupported part. That helps you rewrite the expression into a supported classroom-friendly form.

7. What is the benefit of CSV export?

CSV export is useful for saving inputs, results, and rule notes in a spreadsheet-friendly format for practice logs, assignments, or revision sets.

8. What is the benefit of PDF export?

PDF export creates a clean printable study page. It helps you keep worked symbolic integrals with explanations for offline review.