+91-87964 74404
FlagBACK
Question icon
Grade 11Integral Calculus

Integrate the following w.r.t x:
1)1/(x^2(1+x^4)^(3/4))
2)x^5(a^3+x^3)^(1/2)

Profile image of Shadow
12 Years agoGrade 11
Answers icon

1 Answer

Profile image of Sumit Majumdar
12 Years ago
Dear student, please find the solutions:
  1. \int \frac{1}{x^{2}\left ( 1+x^{4} \right )^{\frac{3}{4}}}dx=\int \frac{sec^{2}\Theta }{2x^{3}sec^{\frac{3}{2}}\Theta }d\Theta =\frac{1}{2}\int \frac{cos\Theta }{sin^{\frac{3}{2}}\Theta }d\Theta =-\frac{1}{\sqrt{sin\Theta }}=-\frac{\left ( 1+x^{4} \right )^{\frac{1}{4}}}{x}+c
    1. \int \frac{x^{5}}{\left ( a^{3}+x^{3} \right )^{\frac{1}{2}}}dx=\frac{1}{3}\int \left ( u^{\frac{1}{2}}-a^{3}u^{\frac{-1}{2}} \right )du=\frac{2}{9}\left ( a^{3}+x^{3} \right )^{\frac{3}{2}}-2\left ( a^{3}+x^{3} \right )^{\frac{1}{2}}+c
    2. Regards
    3. Sumit

Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 4 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago