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人気のある微分積分 >

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

解

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

解

2 x^{2} ln (x) - x^{2} - \frac{x ln ( x )}{2} + x

解答ステップ

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

部分積分を適用する

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

\int 1 d x = x

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

限度を計算する:

2 x^{2} ln (x) - x^{2} - \frac{1}{2} x ln (x) + x

= 2 x^{2} ln (x) - x^{2} - \frac{1}{2} x ln (x) + x

簡素化

= 2 x^{2} ln (x) - x^{2} - \frac{x ln ( x )}{2} + x

人気の例

integral from x^5 to x^6 of (2t-1)^3

\int_{x^{5}}^{x^{6}} (2 t - 1)^{3} d t

integral from 1 to 3 of (2-3/(x^2))

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

integral from 1 to e of (4(ln(x))^2+x)/x

\int_{1}^{e} \frac{4 ( ln ( x ) ) ^{2} + x}{x} d x

integral from 0 to 1 of x*cos(npix)

\int_{0}^{1} x \cdot cos (nπ x) d x

integral from 1 to 6 of (2/x)

\int_{1}^{6} (\frac{2}{x}) d x