What is the integral from 3 to 7 of t^5ln(t) ?

The integral from 3 to 7 of t^5ln(t) is -29230/9+117649/6 ln(7)-243/2 ln(3)

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integral from 3 to 7 of t^5ln(t)

\int_{3}^{7} t^{5} ln (t) d t

- \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

Solution steps

\int_{3}^{7} t^{5} ln (t) d t

Apply Integration By Parts

: [\frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t]_{3}^{7}

= [\frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t]_{3}^{7}

\int \frac{t ^{5}}{6} d t = \frac{t ^{6}}{36}

= [\frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36}]_{3}^{7}

Compute the boundaries:

- \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

= - \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

\int_{0}^{2} \frac{x ^{2}}{x ^{3} + 3} d x

\int_{0}^{1} x sinh (x) d x

\int_{0}^{3} x^{2} - 3 d x

\int_{0}^{\frac{π}{4}} tan (θ) d θ

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (π \cdot x) d x

What is the integral from 3 to 7 of t^5ln(t) ?
The integral from 3 to 7 of t^5ln(t) is -29230/9+117649/6 ln(7)-243/2 ln(3)