Mathematics

# $\displaystyle\int^1_0\tan^{-1}\left[\dfrac{2x-1}{1+x-x^2}\right]dx=?$

##### ANSWER

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Assertion & Reason Hard
##### ASSERTION

If $f(x) = \displaystyle \int_{1}^{x}\frac{lntdt}{1+t+t^{2}}\left ( x> 0 \right )$ then $f(x) = -f\displaystyle \left ( \frac{1}{x} \right )$

##### REASON

If $f(x) =\displaystyle \int_{1}^{x}\frac{lntdt}{t+1},$ then $f(x)+f\displaystyle \left ( \frac{1}{x} \right )=\frac{1}{2}\left ( lnx \right )^{2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Both Assertion and Reason are incorrect
• D. Assertion is incorrect but Reason is correct

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Solve  $\displaystyle\int log x[log x+2]dx =$ _________$+$c.
• A. $x^2 log x+1$
• B. $2x(log x)^2$
• C. $x[(log x)^2+1)]$
• D. $x(log x)^2$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int$ $\dfrac {dx}{(x^{2}+1)(x+3)}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate $\dfrac x{ \sqrt {1-x^2}}$ w.r.t $x$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Easy
$\int \frac{2x^{2}}{3x^{4}2x} dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020