What is the integral of 3x^3ln(x) ?

The integral of 3x^3ln(x) is 3(1/4 x^4ln(x)-(x^4)/(16))+C

Popular >

integral of 3x^3ln(x)

\int 3 x^{3} ln (x) d x

3 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

Solution steps

\int 3 x^{3} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{3} ln (x) d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x

= 3 (\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x)

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= 3 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16})

Add a constant to the solution

= 3 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

\int \frac{1}{20 x} d x

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

\int cos (2 x) sin^{5} (2 x) d x

\int \frac{1}{x \cdot ( ln ( x ) ) ^{3}} d x

\int (\frac{1}{x ^{2}} + \frac{2}{x ^{3}} + \frac{3}{x ^{4}}) d x

What is the integral of 3x^3ln(x) ?
The integral of 3x^3ln(x) is 3(1/4 x^4ln(x)-(x^4)/(16))+C