What is the integral from x to x^4 of ln(t) ?

The integral from x to x^4 of ln(t) is 4x^4ln(x)-x^4-xln(x)+x

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integral from x to x^4 of ln(t)

\int_{x}^{x^{4}} ln (t) d t

4 x^{4} ln (x) - x^{4} - x ln (x) + x

Solution steps

\int_{x}^{x^{4}} ln (t) d t

Apply Integration By Parts

: [t ln (t) - \int 1 d t]_{x}^{x^{4}}

= [t ln (t) - \int 1 d t]_{x}^{x^{4}}

\int 1 d t = t

= [t ln (t) - t]_{x}^{x^{4}}

Compute the boundaries:

4 x^{4} ln (x) - x^{4} - x ln (x) + x

= 4 x^{4} ln (x) - x^{4} - x ln (x) + x

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What is the integral from x to x^4 of ln(t) ?
The integral from x to x^4 of ln(t) is 4x^4ln(x)-x^4-xln(x)+x