What is the integral of (x^2+7)ln(x) ?

The integral of (x^2+7)ln(x) is ln(x)((x^3)/3+7x)-1/3 ((x^3)/3+21x)+C

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integral of (x^2+7)ln(x)

\int (x^{2} + 7) ln (x) d x

ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x) + C

Solution steps

\int (x^{2} + 7) ln (x) d x

Apply Integration By Parts

: ln (x) (\frac{x ^{3}}{3} + 7 x) - \int \frac{1}{3} (x^{2} + 21) d x

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \int \frac{1}{3} (x^{2} + 21) d x

\int \frac{1}{3} (x^{2} + 21) d x = \frac{1}{3} (\frac{x ^{3}}{3} + 21 x)

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x)

Add a constant to the solution

= ln (x) (\frac{x ^{3}}{3} + 7 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 21 x) + C

\int \frac{1 + x}{1 - x} d x

\int \frac{x ^{2} + 2 x - 1}{2 x ^{3} + 3 x ^{2} - 2 x} d x

\frac{d}{d x} (x^{2} - 5 x + 4)

\frac{d y}{d x} = y^{2} - 9, y (5) = 3

\frac{\partial}{\partial x} (u)

What is the integral of (x^2+7)ln(x) ?
The integral of (x^2+7)ln(x) is ln(x)((x^3)/3+7x)-1/3 ((x^3)/3+21x)+C