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Popular >

integral of (3tan(x))/(cos(x))

Solution

\int \frac{3 tan ( x )}{cos ( x )} d x

Solution

3 sec (x) + C

Solution steps

\int \frac{3 tan ( x )}{cos ( x )} d x

Take the constant out:

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

= 3 \cdot \int \frac{tan ( x )}{cos ( x )} d x

Rewrite using trig identities

= 3 \cdot \int tan (x) sec (x) d x

Apply u-substitution

: \int 1 d u

= 3 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 3 \cdot 1 \cdot u

Substitute back

u = sec (x)

= 3 \cdot 1 \cdot sec (x)

Simplify

= 3 sec (x)

Add a constant to the solution

= 3 sec (x) + C

Popular Examples

integral of y/(3y^2+1)

\int \frac{y}{3 y ^{2} + 1} d y

integral of 6/(7+y^2)

\int \frac{6}{7 + y ^{2}} d y

integral of y/(x(2-x^2))

\int \frac{y}{x ( 2 - x ^{2} )} d x

integral of (4x)/(sqrt(2x^2+3))

\int \frac{4 x}{2 x ^{2} + 3} d x

integral of x/(x^2+6x+8)

\int \frac{x}{x ^{2} + 6 x + 8} d x

Frequently Asked Questions (FAQ)

What is the integral of (3tan(x))/(cos(x)) ?
The integral of (3tan(x))/(cos(x)) is 3sec(x)+C