What is the integral of (3sin(x))/(cos^2(x)) ?

The integral of (3sin(x))/(cos^2(x)) is 3sec(x)+C

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integral of (3sin(x))/(cos^2(x))

\int \frac{3 sin ( x )}{cos ^{2} ( x )} d x

3 sec (x) + C

Solution steps

\int \frac{3 sin ( x )}{cos ^{2} ( 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{sin ( x )}{cos ^{2} ( x )} d x

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= 3 \cdot \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= 3 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 3 (- (- \frac{1}{u}))

Substitute back

u = cos (x)

= 3 (- (- \frac{1}{cos ( x )}))

Simplify

3 (- (- \frac{1}{cos ( x )})) : 3 sec (x)

= 3 sec (x)

Add a constant to the solution

= 3 sec (x) + C

\frac{\partial}{\partial y} (ln (x + y))

\frac{d y}{d x} = x x - 24

x^{2} + y^{2} = 29, (2, - 5)

\frac{d}{d x} (3 ln (x) - 5)

What is the integral of (3sin(x))/(cos^2(x)) ?
The integral of (3sin(x))/(cos^2(x)) is 3sec(x)+C