integral from 2 to 4 of x/((x^2+5)^3)

해법

\int_{2}^{4} \frac{x}{( x ^{2} + 5 ) ^{3}} d x

\frac{10}{3969}

십진법

0.00251 \dots

솔루션 단계

\int_{2}^{4} \frac{x}{( x ^{2} + 5 ) ^{3}} d x

대체 적용

: \int_{9}^{21} \frac{1}{2 u ^{3}} d u

= \int_{9}^{21} \frac{1}{2 u ^{3}} d u

정수를 빼라:

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

= \frac{1}{2} \cdot \int_{9}^{21} \frac{1}{u ^{3}} d u

전원 규칙 적용

: [- \frac{1}{2 u ^{2}}]_{9}^{21}

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{9}^{21}

경계 계산:

\frac{20}{3969}

= \frac{1}{2} \cdot \frac{20}{3969}

단순화

= \frac{10}{3969}