What is the integral of 20θsec^2(θ) ?

The integral of 20θsec^2(θ) is 20(θtan(θ)+ln|cos(θ)|)+C

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integral of 20θsec^2(θ)

\int 20 θ sec^{2} (θ) d θ

20 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 20 θ sec^{2} (θ) d θ

Take the constant out:

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

= 20 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 20 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 20 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 20 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 20 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

\int \frac{\frac{d}{1} ( x )}{x} d x

\frac{d}{d x} (\frac{x}{a ^{2} + x ^{2}})

\frac{d}{d x} (16 x + 1)

3 t - 5

t y^{^{'}} + y = 2 t

What is the integral of 20θsec^2(θ) ?
The integral of 20θsec^2(θ) is 20(θtan(θ)+ln|cos(θ)|)+C