integrate x^n
The expression: <math><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></math> contains several variables so we pick <m>x</m> for integral computation Let's compute the integral: <math><mo>∫(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)dx</mo></math> Use the integration formula for <math><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></math>: <math><mo>∫(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)dx</mo><mo> = </mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow></msup></mrow><mrow><mi>n</mi><mo> + </mo><mn>1</mn></mrow></mfrac></math> <math><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow></msup></mrow><mrow><mi>n</mi><mo> + </mo><mn>1</mn></mrow></mfrac></math> Indefinite integrals are defined up to an additive constant <m>C</m>, so this yields: <math><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow></msup></mrow><mrow><mi>n</mi><mo> + </mo><mn>1</mn></mrow></mfrac><mo> + </mo><mi>C</mi></math> ▷<b>Result: <math><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow></msup></mrow><mrow><mi>n</mi><mo> + </mo><mn>1</mn></mrow></mfrac><mo> + </mo><mi>C</mi></math></b><span style='font-size:smaller'>, with <m>C</m> being any constant (computation took 5 steps and 4 ms)</span>
