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Popular >

integral of 5tan^2(x)

Solution

\int 5 tan^{2} (x) d x

Solution

5 (- x + tan (x)) + C

Solution steps

\int 5 tan^{2} (x) d x

Take the constant out:

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

= 5 \cdot \int tan^{2} (x) d x

Rewrite using trig identities

= 5 \cdot \int - 1 + sec^{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

= 5 (- \int 1 d x + \int sec^{2} (x) d x)

\int 1 d x = x

\int sec^{2} (x) d x = tan (x)

= 5 (- x + tan (x))

Add a constant to the solution

= 5 (- x + tan (x)) + C

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Frequently Asked Questions (FAQ)

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