Mathematics

$$\int(tanx -cotx)^{2}dx= $$


ANSWER

$$tanx-cotx-4x+cc$$


SOLUTION
Now,
$$\displaystyle\int (\tan x-\cot x)^2 dx$$
$$=\displaystyle\int (\tan^2x-2+\cot^2x)dx$$
$$=\displaystyle\int (\sec^2x-4+\cos ec^2x)dx$$
$$=\tan x-4x-\cot x+c$$. [ Where $$c$$ is integrating constant]
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Solve 
$$I=\int_{-\pi}^{\pi}{\dfrac{2x(\sin x+1)}{1+\cos^{2}x}dx}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
lf $$\displaystyle \int f(x)\sin x\cos x\>dx=\frac{1}{2(b^{2}-a^{2})}\log(f(x))+c$$, then $$\displaystyle f(x)$$ is equal to
  • A. $$\displaystyle \frac {2 \cos2x}{(b^2-a^2)}$$
  • B. $$\displaystyle \frac{-2 \sec2x}{(b^2-a^2)}$$
  • C. $$\displaystyle \frac {-2 \cos2x}{(b^2-a^2)}$$
  • D. $$\displaystyle \frac {2 \sec2x}{(b^2-a^2)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate $$\int_1^4 {\left( {{x^2} - x} \right)} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Prove that:
$$\displaystyle \int  _{ 0 }^{ \pi /2 }{ \cfrac { 1 }{ 1+\tan ^{ 3 }{ x }  } dx } =\cfrac { \pi  }{ 4 } \quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let g(x) =$$\displaystyle \int_{0}^{x}f\left ( t \right )dt,$$ where f is a function
whose graph is show adjacently.
On the basis of above information, answer te following questions.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer