1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lianna [129]
4 years ago
11

Anti-Derivative ∫(1 + tan²x) dx

Mathematics
1 answer:
8_murik_8 [283]4 years ago
8 0
If you're using the app, try seeing this answer through your broswer:  brainly.com/question/2822785

________________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\!(1+tan^2\,x)\,dx}\\\\\\ \mathsf{=\displaystyle\int\!\bigg[1+\left(\frac{sin\,x}{cos\,x}\right)^{\!2}\bigg]dx}\\\\\\
\mathsf{=\displaystyle\int\!\bigg[1+\frac{sin^2\,x}{cos^2\,x}\bigg]dx}


Reduce both terms to the same common denominator:

\mathsf{=\displaystyle\int\!\bigg[\frac{cos^2\,x}{cos^2\,x}+\frac{sin^2\,x}{cos^2\,x}\bigg]dx}\\\\\\
\mathsf{=\displaystyle\int\!\frac{cos^2\,x+sin^2\,x}{cos^2\,x}\,dx\qquad\quad (but~~cos^2\,x+sin^2\,x=1)}\\\\\\
\mathsf{=\displaystyle\int\! \frac{1}{cos^2\,x}\,dx}\\\\\\
\mathsf{=\displaystyle\int\! sec^2\,x\,dx}


and that last one is an immediate integral:

\mathsf{\displaystyle\int\! sec^2\,x\,dx=tan\,x+C}


Therefore,

\mathsf{\displaystyle\int\! (1+tan^2\,x)\,dx=tan\,x+C}           ✔


I hope this helps. =)


Tags:  <em>indefinite integral anti-derivative trigonometric trig function tangent secant sine cosine tan sec sin cos differential integral calculus</em>

You might be interested in
The vertices of trapezoid ABCD are A(3,3), B(4,3), C(4,2) and D(2,2).
Free_Kalibri [48]

Answer:

I don't get it what is question trying to say

5 0
3 years ago
A plumber earns $50 for a repair job, plus an additional $75 per hour he works. On Tuesday, he completed 3 repair jobs and earne
VLD [36.1K]

Answer:

150 + 75h > 600

Step-by-step explanation:

The inequality that can be used to determine h is shown below:-

As per the given situation,  it is mentioned that a plumber could earns $50 for a repair job, so for three jobs he earned $150 as a total amount

Now

We presume h be the number of hours

Also he earns additional $75 per hour worked so $75

Total amount is $150 + $75h)

The total amount is more than $600

So, the inequality equation is as given below:

150 + 75h > 600

5 0
4 years ago
Apply the commutative property to 13 x 7 x 21 to rearrange the terms and still get the same solution.
Mumz [18]
Answer is D. 21 x 7 x 13

<span>commutative property: </span>changing order of the numbers
3 0
3 years ago
Read 2 more answers
Will give brainliest! And 100 points!!! Plz help. Pic attached
mylen [45]

Step-by-step explanation:

5

4 0
4 years ago
Read 2 more answers
Z^5=-7776i
Sloan [31]

Answer:

Z=+6

Step-by-step explanation:

Z^5=-7776i

Let's note that i I mathematics means negative one i.e

i = -1

So the equation is equal to

Z^5=-*-(7776)

Z^5 = 7776

Z= 5√7776

Since it's a divisible by 6

It's giving us a clue that 6 it's the answer.

Ok let's check the 5th root of 7776 in our calculator.

Z=+6

+6 is the solution to the equation

Z^5=-7776i

7 0
4 years ago
Other questions:
  • Using the z table, find the critical value for a=0.024 in a left tailed test
    14·1 answer
  • How many two digit numbers have one odd digit and one even digit?
    14·2 answers
  • A chef had 5 limes. How many containers of lime juice could she make if each container used 1/3 of a lime
    11·1 answer
  • Can anyone help me on this
    10·1 answer
  • art bought 4 boxes of pens but gave his friend ben 8 pens and now has a total of 112 pens how many are in a box? which of the fo
    10·2 answers
  • A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
    8·1 answer
  • (3x^-4)6/9x^-12 can you please solve? I’ll give brainly
    10·1 answer
  • Which postulate proves these two
    9·1 answer
  • PLZ HELP ILL MARK AS BRAINLIETS
    11·2 answers
  • How write 632.745 word form
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!