What is the integral of 4θsec^2(θ) ?

The integral of 4θsec^2(θ) is 4(θtan(θ)+ln|cos(θ)|)+C

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integral of 4θsec^2(θ)

\int 4 θ sec^{2} (θ) d θ

4 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

Solution steps

\int 4 θ sec^{2} (θ) d θ

Take the constant out:

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

= 4 \cdot \int θ sec^{2} (θ) d θ

Apply Integration By Parts

: θ tan (θ) - \int tan (θ) d θ

= 4 (θ tan (θ) - \int tan (θ) d θ)

\int tan (θ) d θ = - ln ∣ cos (θ) ∣

= 4 (θ tan (θ) - (- ln ∣ cos (θ) ∣))

Simplify

= 4 (θ tan (θ) + ln ∣ cos (θ) ∣)

Add a constant to the solution

= 4 (θ tan (θ) + ln ∣ cos (θ) ∣) + C

y^{^{'}} = - \frac{y ^{2}}{( 0.05 + y )}, y (0) = 9

\int \frac{1}{2} x^{\frac{3}{4}} d x

\int (9) d x

y = x^{2} + 19 x^{9}

x \to \infty lim (8 + \frac{1}{x})

What is the integral of 4θsec^2(θ) ?
The integral of 4θsec^2(θ) is 4(θtan(θ)+ln|cos(θ)|)+C