This integration seems easy!

Calculus Level 5

f ( x ) = ∫ d x ( x + 2 ) 4 + ( x + 4 ) 4 + 14 \large{ f(x) = \int \dfrac{dx}{(x+2)^4 + (x+4)^4 + 14} }

Let f ( x ) f(x) be a function defined as above such that f ( − 3 ) = 0 f(-3) = 0 holds true. Then find the value of f ( 0 ) f(0) upto three decimal places.


The answer is 0.076.

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Satyajit Mohanty by Satyajit Mohanty , 24, India

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1 solution

Put (x+3) as t.Then the denominator gets factorised nicely.The integral can be split into two simple integrals by using partial fractions.

6 Helpful 0 Interesting 2 Brilliant 0 Confused

wow that is actually easier than what i did, nice solution sir.

Mardokay Mosazghi - 5 years, 3 months ago

What makes you think it would be the right substitution.

Deepesh Pandey - 5 years, 1 month ago

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Just do it and observe things simplify greatly.

Indraneel Mukhopadhyaya - 5 years, 1 month ago

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