Calculus Examples

$\int_{0}^{9 \ln (x)} e^{t} d t$

Step 1

The integral of $e^{t}$ with respect to $t$ is $e^{t}$ .

$e^{t}]_{0}^{9 \ln (x)}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $e^{t}$ at $9 \ln (x)$ and at $0$ .

$(e^{9 \ln (x)}) - e^{0}$

Step 2.2

Simplify.

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Step 2.2.1

Anything raised to $0$ is $1$ .

$e^{9 \ln (x)} - 1 \cdot 1$

Step 2.2.2

Multiply $- 1$ by $1$ .

$e^{9 \ln (x)} - 1$

Step 3

Simplify each term.

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Step 3.1

Simplify $9 \ln (x)$ by moving $9$ inside the logarithm.

$e^{\ln (x^{9})} - 1$

Step 3.2

Exponentiation and log are inverse functions.

$x^{9} - 1$