What is the integral of t^6ln(t) ?

The integral of t^6ln(t) is 1/7 t^7ln(t)-(t^7)/(49)+C

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integral of t^6ln(t)

\int t^{6} ln (t) d t

\frac{1}{7} t^{7} ln (t) - \frac{t ^{7}}{49} + C

Solution steps

\int t^{6} ln (t) d t

Apply Integration By Parts

: \frac{1}{7} t^{7} ln (t) - \int \frac{t ^{6}}{7} d t

= \frac{1}{7} t^{7} ln (t) - \int \frac{t ^{6}}{7} d t

\int \frac{t ^{6}}{7} d t = \frac{t ^{7}}{49}

= \frac{1}{7} t^{7} ln (t) - \frac{t ^{7}}{49}

Add a constant to the solution

= \frac{1}{7} t^{7} ln (t) - \frac{t ^{7}}{49} + C

f (x) = (2 - 3 x)^{3}

\int sin (x) - 4 cos (x) + 1 d x

\int g \cdot \frac{m}{k} (1 - e^{- \frac{k}{m} \cdot t}) d t

x \to \frac{5 π}{3} lim (cos (x))

f (x) = x^{3} - x^{2}, at x = - 1

What is the integral of t^6ln(t) ?
The integral of t^6ln(t) is 1/7 t^7ln(t)-(t^7)/(49)+C