Calculus Examples

$\int_{0}^{1} (3 \tan (x)) d x$

Step 1

Remove parentheses.

$\int_{0}^{1} 3 \tan (x) d x$

Step 2

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int_{0}^{1} \tan (x) d x$

Step 3

The integral of $\tan (x)$ with respect to $x$ is $\ln (| \sec (x) |)$ .

$3 (\ln (| \sec (x) |)]_{0}^{1})$

Step 4

Simplify the answer.

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Step 4.1

Evaluate $\ln (| \sec (x) |)$ at $1$ and at $0$ .

$3 (\ln (| \sec (1) |) - \ln (| \sec (0) |))$

Step 4.2

Simplify.

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Step 4.2.1

The exact value of $\sec (0)$ is $1$ .

$3 (\ln (| \sec (1) |) - \ln (| 1 |))$

Step 4.2.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$3 \ln (\frac{| \sec (1) |}{| 1 |})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \ln (\frac{| \sec (1) |}{| 1 |})$

Decimal Form:

$0.00045694 \dots$