What is the integral from 1 to t of (21)/(x^3) ?

The integral from 1 to t of (21)/(x^3) is 21(-1/(2t^2)+1/2)

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integral from 1 to t of (21)/(x^3)

\int_{1}^{t} \frac{21}{x ^{3}} d x

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

Solution steps

\int_{1}^{t} \frac{21}{x ^{3}} d x

Take the constant out:

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

= 21 \cdot \int_{1}^{t} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{t}

= 21 [- \frac{1}{2 x ^{2}}]_{1}^{t}

Compute the boundaries:

- \frac{1}{2 t ^{2}} + \frac{1}{2}

= 21 (- \frac{1}{2 t ^{2}} + \frac{1}{2})

9 x^{- 4}

\int \frac{1 + x}{1 - 2 x - x ^{2}} d x

690 (1 - (\frac{x}{345})^{2})

\int \frac{100}{36 + 25 x ^{2}} d x

n = 1 \sum \infty n e^{- n}

What is the integral from 1 to t of (21)/(x^3) ?
The integral from 1 to t of (21)/(x^3) is 21(-1/(2t^2)+1/2)