Mathematics

$$\displaystyle\int \frac{x^{3}}{25x^{8}-16}dx.$$


ANSWER

$$\displaystyle \frac{1}{160}\log \frac{5x^{4}-4}{5x^{4}+4}$$


SOLUTION
Let $$\displaystyle I=\int  \frac { x^{ 3 } }{ 25x^{ 8 }-16 } dx$$
Put $$\displaystyle 5x^{ 4 }=t\Rightarrow 20x^{ 3 }dx=dt$$

$$\displaystyle I=\frac { 1 }{ 20 } \int  \frac { dt }{ t^{ 2 }-4^{ 2 } } =\frac { 1 }{ 20 } .\frac { 1 }{ 2.4 } \log  \frac { t-4 }{ t+4 } $$

$$\displaystyle =\frac { 1 }{ 160 } \log  \frac { 5x^{ 4 }-4 }{ 5x^{ 4 }+4 } $$
Hence, option 'C' is correct.
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
Evaluate $$\displaystyle \int_{0}^{1}{}{(2x^2 +x+1)}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
Evaluate: $$\int{(P+Q)}$$ $$dx$$
  • A. $$\int{P}dx +Q+C$$
  • B. $$\int{P}dx-\int{Q}dx$$
  • C. None of the above
  • D. $$\int{P}dx+\int{Q}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
$$\text { Evaluate: }\displaystyle \int \dfrac{d x}{x\left(x^{5}+3\right)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Integrate with respect to $$x$$:
$$x\ ln\ x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate $$\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer