Evaluate using formulas and rules of \int (200)/(x^3)

-\frac{100}{x^{2}}+C,C \in \mathbb{R}

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Question :

int (200)/(x^3)

- \frac{100}{x ^{2}} + C, C \in R

Evaluate

\int 200 \div x^{3} d x

Rewrite the expression

\int \frac{200}{x ^{3}} d x

Rewrite the expression

\int 200 \times \frac{1}{x ^{3}} d x

Use the property of integral \int k f (x) d x = k \int f (x) d x

200 \times \int \frac{1}{x ^{3}} d x

Use the property of integral \int x^{n} d x = \frac{x ^{n + 1}}{n + 1}

200 \times \frac{x ^{- 3 + 1}}{- 3 + 1}

Add the numbers

200 \times \frac{x ^{- 2}}{- 3 + 1}

Add the numbers

200 \times \frac{x ^{- 2}}{- 2}

Divide the terms

More Steps

Evaluate

\frac{x ^{- 2}}{- 2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{x ^{- 2}}{2}

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

- \frac{\frac{1}{x ^{2}}}{2}

Simplify

- \frac{1}{2 x ^{2}}

200 (- \frac{1}{2 x ^{2}})

Multiplying or dividing an odd number of negative terms equals a negative

- 200 \times \frac{1}{2 x ^{2}}

Cancel out the common factor 2

- 100 \times \frac{1}{x ^{2}}

Multiply the terms

- \frac{100}{x ^{2}}

Solution

- \frac{100}{x ^{2}} + C, C \in R

Show Solution

Evaluate using formulas and rules of $\int (200)/(x^3)$

$- \frac{100}{x ^{2}} + C, C \in R$

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