What is the integral of (4/(cos^2(x))-5/(sin^2(x))) ?

The integral of (4/(cos^2(x))-5/(sin^2(x))) is 4tan(x)+5cot(x)+C

Popular >

integral of (4/(cos^2(x))-5/(sin^2(x)))

\int (\frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{2} ( x )}) d x

4 tan (x) + 5 cot (x) + C

Solution steps

\int \frac{4}{cos ^{2} ( x )} - \frac{5}{sin ^{2} ( x )} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{4}{cos ^{2} ( x )} d x - \int \frac{5}{sin ^{2} ( x )} d x

\int \frac{4}{cos ^{2} ( x )} d x = 4 tan (x)

\int \frac{5}{sin ^{2} ( x )} d x = - 5 cot (x)

= 4 tan (x) - (- 5 cot (x))

Simplify

= 4 tan (x) + 5 cot (x)

Add a constant to the solution

= 4 tan (x) + 5 cot (x) + C

(\frac{1}{y ^{2}} - \frac{2}{y ^{4}}) (y + 8 y^{3})

\int_{- 2}^{3} \frac{35}{x ^{4}} d x

\frac{d y}{d x} = e^{2 x} + 7 y

\frac{d}{d x} (\frac{y}{x - y})

y = 2 x^{3} - x^{2} + 9, (2, 21)

What is the integral of (4/(cos^2(x))-5/(sin^2(x))) ?
The integral of (4/(cos^2(x))-5/(sin^2(x))) is 4tan(x)+5cot(x)+C