Calculus Examples

$\int 2 t^{- 8} d t$

Step 1

Since $2$ is constant with respect to $t$ , move $2$ out of the integral.

$2 \int t^{- 8} d t$

Step 2

By the Power Rule, the integral of $t^{- 8}$ with respect to $t$ is $- \frac{1}{7} t^{- 7}$ .

$2 (- \frac{1}{7} t^{- 7} + C)$

Step 3

Simplify the answer.

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Step 3.1

Simplify.

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Step 3.1.1

Combine $t^{- 7}$ and $\frac{1}{7}$ .

$2 (- \frac{t^{- 7}}{7} + C)$

Step 3.1.2

Move $t^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 (- \frac{1}{7 t^{7}} + C)$

Step 3.2

Simplify.

$2 (- \frac{1}{7 t^{7}}) + C$

Step 3.3

Simplify.

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Step 3.3.1

Multiply $- 1$ by $2$ .

$- 2 \frac{1}{7 t^{7}} + C$

Step 3.3.2

Combine $- 2$ and $\frac{1}{7 t^{7}}$ .

$\frac{- 2}{7 t^{7}} + C$

Step 3.3.3

Move the negative in front of the fraction.

$- \frac{2}{7 t^{7}} + C$