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受欢迎的微积分 >

integral of tln(t+2)

解答

\int t ln (t + 2) d t

解答

ln (t + 2) (\frac{1}{2} (t + 2)^{2} - 2 (t + 2)) - \frac{1}{4} (t^{2} - 4 t - 12) + C

求解步骤

\int t ln (t + 2) d t

使用换元积分法

= \int (u - 2) ln (u) d u

使用分布积分法

= ln (u) (\frac{u ^{2}}{2} - 2 u) - \int \frac{1}{2} (u - 4) d u

\int \frac{1}{2} (u - 4) d u = \frac{1}{2} (\frac{u ^{2}}{2} - 4 u)

= ln (u) (\frac{u ^{2}}{2} - 2 u) - \frac{1}{2} (\frac{u ^{2}}{2} - 4 u)

u = t + 2

代回

= ln (t + 2) (\frac{( t + 2 ) ^{2}}{2} - 2 (t + 2)) - \frac{1}{2} (\frac{( t + 2 ) ^{2}}{2} - 4 (t + 2))

化简

ln (t + 2) (\frac{( t + 2 ) ^{2}}{2} - 2 (t + 2)) - \frac{1}{2} (\frac{( t + 2 ) ^{2}}{2} - 4 (t + 2)) : ln (t + 2) (\frac{1}{2} (t + 2)^{2} - 2 (t + 2)) - \frac{1}{4} (t^{2} - 4 t - 12)

= ln (t + 2) (\frac{1}{2} (t + 2)^{2} - 2 (t + 2)) - \frac{1}{4} (t^{2} - 4 t - 12)

解答补常数

= ln (t + 2) (\frac{1}{2} (t + 2)^{2} - 2 (t + 2)) - \frac{1}{4} (t^{2} - 4 t - 12) + C

作图

流行的例子

d/(dt)(sin(5t))

\frac{d}{d t} (sin (5 t))

y^{^{'}} = 2 x - 3 y

integral of 2(tan^2(x)+tan^4(x))

\int 2 (tan^{2} (x) + tan^{4} (x)) d x

integral of xarccot(x)

\int x arccot (x) d x

f^{''}(x)=x^{-3/2},f^'(4)=7,f(0)=0

f^{^{''}} (x) = x^{- \frac{3}{2}}, f^{^{'}} (4) = 7, f (0) = 0