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

The integral from x to 2x^2 of ln(t) is 2ln(2)x^2+4x^2ln(x)-2x^2-xln(x)+x

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integral from x to 2x^2 of ln(t)

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

2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

= 2 ln (2) x^{2} + 4 x^{2} ln (x) - 2 x^{2} - x ln (x) + x

\int_{- 2}^{2} 3 x^{2} + 2 x d x

\int_{0}^{1} (4 x^{3} + 5) d x

\int_{1}^{2} \frac{1}{2 - 3 x} d x

\int_{0}^{s i n (2 x)} arcsin (x) d x

\int_{0}^{3} \frac{x}{1 + x} d x

What is the integral from x to 2x^2 of ln(t) ?
The integral from x to 2x^2 of ln(t) is 2ln(2)x^2+4x^2ln(x)-2x^2-xln(x)+x