What is the integral of 7tan^2(x) ?

The integral of 7tan^2(x) is 7(-x+tan(x))+C

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integral of 7tan^2(x)

\int 7 tan^{2} (x) d x

7 (- x + tan (x)) + C

Solution steps

\int 7 tan^{2} (x) d x

Take the constant out:

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

= 7 \cdot \int tan^{2} (x) d x

Rewrite using trig identities

= 7 \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

= 7 (- \int 1 d x + \int sec^{2} (x) d x)

\int 1 d x = x

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

= 7 (- x + tan (x))

Add a constant to the solution

= 7 (- x + tan (x)) + C

6 e^{5 t} cos (2 t) - e^{7 t}

- 7 e^{- 3 x} - 6 e^{- 3 x} x

arctan (x^{10})

f (x) = x^{2} + 3, (- 5, 28)

10 y^{^{''}} - 10 y^{^{'}} + 5 y = 0