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Solve the integral

1x2+9dx

Short Answer

Expert verified

sinh-1x3+c

Step by step solution

01

Step 1. Given 

The given integral is1x2+9dx.

02

Step 2. Simplifying the integral using identity

Tosolvetheintegral,letx=3sinh(u).Now,derivationoftheaboveequationissolvedbelow.x=3sinh(u).dx=cosh(u)duNow,usetheidentitysinh2(u)+1=cosh2(u)1x2+9dx=1(3sinh(u).2)+9dx=13cosh2(u)dx=1cosh(u)

03

Step 3. Solving the integral

1x2+9dx=1du=u=sinh-1x3+c

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