What is the integral from x to x^4 of t^5 ?

The integral from x to x^4 of t^5 is (x^{24}-x^6)/6

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integral from x to x^4 of t^5

\int_{x}^{x^{4}} t^{5} d t

\frac{x ^{24} - x ^{6}}{6}

Solution steps

\int_{x}^{x^{4}} t^{5} d t

Apply the Power Rule

: [\frac{t ^{6}}{6}]_{x}^{x^{4}}

= [\frac{t ^{6}}{6}]_{x}^{x^{4}}

Compute the boundaries:

\frac{x ^{24}}{6} - \frac{x ^{6}}{6}

= \frac{x ^{24}}{6} - \frac{x ^{6}}{6}

Simplify

= \frac{x ^{24} - x ^{6}}{6}

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What is the integral from x to x^4 of t^5 ?
The integral from x to x^4 of t^5 is (x^{24}-x^6)/6