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

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

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integral of (7+7tan^2(θ))

\int (7 + 7 tan^{2} (θ)) d θ

7 tan (θ) + C

Solution steps

\int 7 + 7 tan^{2} (θ) d θ

7 + 7 tan^{2} (θ) = 7 (1 + tan^{2} (θ))

= \int 7 (1 + tan^{2} (θ)) d θ

Take the constant out:

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

= 7 \cdot \int 1 + tan^{2} (θ) d θ

Rewrite using trig identities

= 7 \cdot \int sec^{2} (θ) d θ

Use the common integral:

\int sec^{2} (θ) d θ = tan (θ)

= 7 tan (θ)

Add a constant to the solution

= 7 tan (θ) + C

\frac{d}{d x} (\frac{x ^{4} - 3 x ^{3} - 6 x ^{2} - 3 x + 2}{x})

f (x) = \frac{x}{( 2 x - 1 ) ^{6}}, at x = 1

\frac{d y}{d x} + 3 y + 5 = 0

cos (2 x)

\frac{d}{d x} (\frac{1}{7 x + 1})

What is the integral of (7+7tan^2(θ)) ?
The integral of (7+7tan^2(θ)) is 7tan(θ)+C