Mathematics

$\displaystyle \int \frac{x^{5/2}}{\sqrt{1+x^{7}}}dx \displaystyle =\frac{1}{k}log\left ( x^{k}+\sqrt{1+x^{7}} \right )+C$

3.5

SOLUTION
Substitute $\displaystyle x^{7/2}=t$
$\displaystyle \therefore \frac{7}{2}x^{5/2}dx=dt$
$\displaystyle \therefore I=\int \frac{2}{7}\frac{dt}{\sqrt{1+t^{2}}}=\frac{2}{7}log\left ( t+\sqrt{1+t^{2}} \right )+C$
$\displaystyle =\frac{2}{7}log\left ( x^{7/2}+\sqrt{1+x^{7}} \right )+C$

Its FREE, you're just one step away

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

Realted Questions

Q1 Single Correct Medium

$\displaystyle \frac{x^{2}+5x+7}{(x-3)^{3}}=\frac{A}{x-3}+\frac{B}{(x-3)^{2}}+\frac{C}{(x-3)^{3}}\Rightarrow A=$
• A. 2
• B. -3
• C. 4
• D. 1

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
$\displaystyle I= \int_{0}^{\pi }\frac{x\tan x}{\sec x+\tan x}dx= \frac{\pi }{C}\left ( \pi -2 \right ).$
What is C?

1 Verified Answer | Published on 17th 09, 2020

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

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int {\cfrac{{{x^3} + {x^2} + 1}}{{{x} + 1}}dx}$

Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$