$\displaystyle\int \sec 3x\tan 3x\ dx=\int\dfrac{1}{\cos 3x}\cdot\dfrac{\sin 3x}{\cos 3x}\ dx=\int\dfrac{\sin 3x}{\cos^23x}\ dx\\\\\Rightarrow \left|\begin{array}{ccc}\cos 3x=t\\-3\sin 3x\ dx=dt\\\sin 3x\ dx=-\frac{1}{3}\ dt\end{array}\right|\Rightarrow\int\left(-\dfrac{1}{3t^2}\right)dt=-\dfrac{1}{3}\int t^{-2}\ dt\\\\=-\dfrac{1}{3}(-t^{-1})+C=\dfrac{1}{3t}+C=\dfrac{1}{3\cos 3x}+C\\\\Answer:\boxed{\int \sec 3x\tan 3x\ dx=\dfrac{1}{3\cos 3x}+C}$

3 0

4 years ago

Read 2 more answers

Shelley spent 17 minutes washing the dishes. She spent 38 minutes cleaning her room. Explain how you can use mental math to find

ddd [48]

Ew, mental math... so basically, we would estimate the washing dishes to 20 minutes, and cleaning 40 min,
together 20+40 min

is 60 minutes, aprox 1 hour

Shelly spent almost 1 hour cleaning

5 0

3 years ago

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At the farmers' market, Lillian bought 5/12 of a pound of string beans and 1/12 of a pound of lima beans. How many more pounds o

Ronch [10]

Answer:

1/3 more pounds of string beans.

Step-by-step explanation:

Amount of string beans: 5/12 of a lbs(pound)

Amount of lima beans: 1/12 of a lbs

Amount of string beans - Amount of lima beans = 5/12-1/12 =4/12 which simplifies down to 1/3.

7 0

3 years ago

Find the probability that of 25 randomly selected students no two share the same birthday

lina2011 [118]

Answer:12.5

Step-by-step explanation:

8 0

3 years ago