What is the integral of (0.8(3+ln(u))^3)/u ?

The integral of (0.8(3+ln(u))^3)/u is 0.2(3+ln(u))^4+C

Popular >

integral of (0.8(3+ln(u))^3)/u

\int \frac{0.8 ( 3 + ln ( u ) ) ^{3}}{u} d u

0.2 (3 + ln (u))^{4} + C

Solution steps

\int \frac{0.8 ( 3 + ln ( u ) ) ^{3}}{u} d u

Take the constant out:

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

= 0.8 \cdot \int \frac{( 3 + ln ( u ) ) ^{3}}{u} d u

Apply u-substitution

: \int v^{3} d v

= 0.8 \cdot \int v^{3} d v

Apply the Power Rule

: \frac{v ^{4}}{4}

= 0.8 \cdot \frac{v ^{4}}{4}

Substitute back

v = 3 + ln (u)

= 0.8 \cdot \frac{( 3 + ln ( u ) ) ^{4}}{4}

Simplify

0.8 \cdot \frac{( 3 + ln ( u ) ) ^{4}}{4} : 0.2 (3 + ln (u))^{4}

= 0.2 (3 + ln (u))^{4}

Add a constant to the solution

= 0.2 (3 + ln (u))^{4} + C

y = 2 x^{3} - 8 x, (2, 0)

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

y = x + 2, y = x^{2}

\frac{d}{d x} (\frac{25 - x ^{2} - y ^{2}}{y})

x \to \frac{π}{2} lim (tan (\frac{x}{2}))

What is the integral of (0.8(3+ln(u))^3)/u ?
The integral of (0.8(3+ln(u))^3)/u is 0.2(3+ln(u))^4+C