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Popular >

integral of (3sec(x)tan(x)-5csc^2(x))

Solution

\int (3 sec (x) tan (x) - 5 csc^{2} (x)) d x

Solution

3 sec (x) + 5 cot (x) + C

Solution steps

\int 3 sec (x) tan (x) - 5 csc^{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 3 sec (x) tan (x) d x - \int 5 csc^{2} (x) d x

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

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

= 3 sec (x) - (- 5 cot (x))

Simplify

= 3 sec (x) + 5 cot (x)

Add a constant to the solution

= 3 sec (x) + 5 cot (x) + C

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\int 4^{u} d u

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n = 1 \sum \infty \frac{2}{2 ^{n}}

integral of x(sin^2(x))

\int x (sin^{2} (x)) d x

2y^{''}+16y^'+32y=0,y(0)=-3,y^'(0)=10

2 y^{^{''}} + 16 y^{^{'}} + 32 y = 0, y (0) = - 3, y^{^{'}} (0) = 10

Frequently Asked Questions (FAQ)

What is the integral of (3sec(x)tan(x)-5csc^2(x)) ?
The integral of (3sec(x)tan(x)-5csc^2(x)) is 3sec(x)+5cot(x)+C