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受欢迎的微积分 >

integral of (-t)/((t+1)-sqrt(t+1))

解答

\int \frac{- t}{( t + 1 ) - t + 1} d t

解答

- t - 1 - 2 t + 1 + C

求解步骤

\int \frac{- t}{t + 1 - t + 1} d t

提出常数:

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

= - \int \frac{t}{t + 1 - t + 1} d t

使用换元积分法

= - \int 2 (u + 1) d u

提出常数:

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

= - 2 \cdot \int u + 1 d u

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - 2 (\int u d u + \int 1 d u)

\int u d u = \frac{u ^{2}}{2}

\int 1 d u = u

= - 2 (\frac{u ^{2}}{2} + u)

u = t + 1

代回

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

化简

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

= - t - 1 - 2 t + 1

解答补常数

= - t - 1 - 2 t + 1 + C

作图

流行的例子

\int 36

derivative of 2sin^3(5x)

\frac{d}{d x} (2 sin^{3} (5 x))

integral of 3x(ln(x^7))^2

\int 3 x (ln (x^{7}))^{2} d x

derivative of arctan((3+x/(3-x)))

\frac{d}{d x} (arctan (\frac{3 + x}{3 - x}))

derivative of x+{z}(x)

\frac{d}{d x} (x + z (x))