What is the integral from 1/5 to 7 of 6xln(5x) ?

The integral from 1/5 to 7 of 6xln(5x) is 6(-306/25+49/2 ln(35))

Popular >

integral from 1/5 to 7 of 6xln(5x)

\int_{\frac{1}{5}}^{7} 6 x ln (5 x) d x

6 (- \frac{306}{25} + \frac{49}{2} ln (35))

Decimal Notation

449.19616 \dots

Solution steps

\int_{\frac{1}{5}}^{7} 6 x ln (5 x) d x

Take the constant out:

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

= 6 \cdot \int_{\frac{1}{5}}^{7} x ln (5 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

= 6 [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 6 [\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}]_{\frac{1}{5}}^{7}

Compute the boundaries:

- \frac{306}{25} + \frac{49}{2} ln (35)

= 6 (- \frac{306}{25} + \frac{49}{2} ln (35))

f (x) = (x^{2} - 9)^{2}

\frac{d y}{d x} = \frac{3 y ^{2} cot ( x ) + sin ( x ) cos ( x )}{2 y}

x \to 10 lim (\frac{8}{( x - 10 ) ^{2}})

\frac{d}{d x} (\frac{2 x + 1}{2 x - 1})

(10 x e^{x} - 5 x y) d x + (2 x y - 5 x^{2}) d y = 0

What is the integral from 1/5 to 7 of 6xln(5x) ?
The integral from 1/5 to 7 of 6xln(5x) is 6(-306/25+49/2 ln(35))