Mathematics

$\int \dfrac{(x^2+1)a^x+\tan^{-1}x}{x^2+1}dx$

$\dfrac{a^x}{\log a}+\dfrac{(\tan^{-1}x)^2}{2}$

SOLUTION

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

Realted Questions

Q1 Single Correct Medium
If $\displaystyle \frac{1}{(1-2\mathrm{x})(1+3\mathrm{x})}$ $=\displaystyle \frac{\mathrm{A}}{1-2\mathrm{x}}+\frac{\mathrm{B}}{1+3\mathrm{x}}$ then $2\mathrm{B}=$
• A. A
• B. 2A
• C. -3A
• D. 3A

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int_{\pi /4}^{\pi /2} Cotx.dx_{=}$
• A. 2 log 2
• B. $\displaystyle \frac{\pi}{2}$ log2
• C. $\log 2$
• D. $\log\sqrt{2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate : $\displaystyle \int \sec x\tan x\sqrt{\sec ^{2}x+1}dx.$
• A. $\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}-\frac{1}{2}\log \left [ t+\sqrt{t^{2}+1} \right ].$ where $t=\sec x$
• B. $\displaystyle t\sqrt{t^{2}+1}+\log \left [ t+\sqrt{t^{2}+1} \right ].$ where $t=\sec x$
• C. $\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}+\frac{1}{2}\log \left [ t-\sqrt{t^{2}+1} \right ].$ where $t=\sec x$
• D. $\displaystyle \frac{1}{2}t\sqrt{t^{2}+1}+\frac{1}{2}\log \left [ t+\sqrt{t^{2}+1} \right ].$ where $t=\sec x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate: $\displaystyle \int{(x-1)} dx$
• A. $\dfrac{x^2}{2} -2x+C$
• B. $\dfrac{x^2}{2} -1+C$
• C. $\dfrac{x^2}{2} -2+C$
• D. $\dfrac{x^2}{2} -x+C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$4 \displaystyle \int \dfrac{\sqrt{a^6 + x^8}}{x} dx$ is equal to ______________________.
• A. $a^6 ln\vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$
• B. $\sqrt{a^6 + x^8} + \dfrac {a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} - a^3} {\sqrt {a^6 + x^8} + a^3}\vert + c$
• C. $a^6 ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$
• D. $\sqrt{a^6 + x^8} + \dfrac{a^3}{2} ln \vert \dfrac {\sqrt{a^6 + x^8} + a^3} {\sqrt {a^6 + x^8} - a^3}\vert + c$