Mathematics

Write a value of 
$$\int { \tan ^{ 6 }{ x }  } \sec ^{ 2 }{ x } dx$$


SOLUTION
Let $$t=\tan{x}\Rightarrow\,dt={\sec}^{2}{x}dx$$

$$I=\displaystyle\int{{\tan}^{6}{x}{\sec}^{2}{x}dx}$$

$$=\displaystyle\int{{t}^{6}dt}$$

$$=\dfrac{{t}^{7}}{7}+c$$

$$=\dfrac{{\tan}^{7}{x}}{7}+c$$    ........where $$t=\tan{x}$$
View Full Answer

Its FREE, you're just one step away


Subjective 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
Evaluate  :    $$I = \int {\dfrac{{x + 9}}{{{x^2} + 5}}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
Evaluate : $$\displaystyle \int_{-\frac{1}{\sqrt2}}^{\frac{1}{\sqrt2}}\frac{x^{8}}{1-x^{4}}\times \left [ \sin ^{-1}\left ( 1-2x^{2} \right ) +\cos ^{-1}\left ( 2x\sqrt{1-x^{2}} \right )\right ]dx$$
  • A. $$\displaystyle \pi \left [ \frac{1}{2}\log \frac{\sqrt{2}+1}{\sqrt{2}-1}+\tan ^{-1} \frac{1}{\sqrt{2}}+\frac{21}{10\sqrt{2}}\right ]$$
  • B. $$\displaystyle \pi \left [ \frac{1}{2}\log \frac{\sqrt{2}-1}{\sqrt{2}-1}+\tan ^{-1} \frac{1}{\sqrt{2}}-\frac{21}{10\sqrt{2}}\right ]$$
  • C. $$\displaystyle \pi \left [ \frac{1}{2}\log \frac{\sqrt{2}-1}{\sqrt{2}-1}+\tan ^{-1} \frac{1}{\sqrt{2}}+\frac{21}{10\sqrt{2}}\right ]$$
  • D. $$\displaystyle \pi \left [ \frac{1}{2}\log \frac{\sqrt{2}+1}{\sqrt{2}-1}+\tan ^{-1} \frac{1}{\sqrt{2}}-\frac{21}{10\sqrt{2}}\right ]$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate
$$\int _{ -1 }^{ 1 }{ { x }^{ 17 } } { cos }^{ 4 }xdx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
If $$\displaystyle\int f(x)dx=g(x),$$ then $$\displaystyle\int f^{-1}(x)dx=$$ _____________$$+$$c.
  • A. $$xf^{-1}(x)-g(f^{-1}(x))$$
  • B. $$xf^{-1}(x)-g(f(x))$$
  • C. $$x\cdot f^{-1}(x)$$
  • D. $$x\cdot f(x)-g(f^{-1}(x))$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer