What is the integral from 2 to 6 of t^3ln(5x) ?

The integral from 2 to 6 of t^3ln(5x) is (2ln(2700)-4)t^3

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integral from 2 to 6 of t^3ln(5x)

\int_{2}^{6} t^{3} ln (5 x) d x

(2 ln (2700) - 4) t^{3}

Solution steps

\int_{2}^{6} t^{3} ln (5 x) d x

Take the constant out:

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

= t^{3} \cdot \int_{2}^{6} ln (5 x) d x

Apply Integration By Parts

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

= t^{3} [x ln (5 x) - \int 1 d x]_{2}^{6}

\int 1 d x = x

= t^{3} [x ln (5 x) - x]_{2}^{6}

Compute the boundaries:

6 ln (30) - 4 - 2 ln (10)

= t^{3} (6 ln (30) - 4 - 2 ln (10))

Simplify

= (2 ln (2700) - 4) t^{3}

\frac{1}{( s ^{2} - 1 )}

\frac{\partial}{\partial x} (7 + x ln (x y - 5))

\frac{d}{d y} (2 y)

\int_{0}^{x} y lo g_{10} (y) d y

n = 3 \sum \infty \frac{4 ^{n}}{7 ^{n}}

What is the integral from 2 to 6 of t^3ln(5x) ?
The integral from 2 to 6 of t^3ln(5x) is (2ln(2700)-4)t^3