What is the integral of tan(10x) ?

The integral of tan(10x) is -1/10 ln|cos(10x)|+C

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integral of tan(10x)

\int tan (10 x) d x

- \frac{1}{10} ln ∣ cos (10 x) ∣ + C

Solution steps

\int tan (10 x) d x

Rewrite using trig identities

= \int \frac{sin ( 10 x )}{cos ( 10 x )} d x

Apply u-substitution

: \int - \frac{1}{10 u} d u

= \int - \frac{1}{10 u} d u

Take the constant out:

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

= - \frac{1}{10} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{10} ln ∣ u ∣

Substitute back

u = cos (10 x)

= - \frac{1}{10} ln ∣ cos (10 x) ∣

Add a constant to the solution

= - \frac{1}{10} ln ∣ cos (10 x) ∣ + C

x \to \infty lim (x - \frac{1}{x})

\int_{1}^{\infty} \frac{6}{x ^{3}} d x

\frac{\partial}{\partial x} (1.2)

y^{^{'}} = 1 + x + y + x y

\int_{6}^{8} \frac{42}{( x - 6 ) ^{3}} d x

What is the integral of tan(10x) ?
The integral of tan(10x) is -1/10 ln|cos(10x)|+C