Originally Posted by

**ArTiCK** Hi,

It says 'using a hyperbolic or trigonometric substitution'

ArTiCk

$\displaystyle \int\left(1+4x^2\right)~dx$

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substitution:

$\displaystyle sin(a) = x$

$\displaystyle cos(a) ~da = ~dx$

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$\displaystyle =\int cos(a)\left(1+4sin^2(a)\right)~da$

$\displaystyle =\int cos(a) ~da + 4 \int cos(a)~sin^2(a)~da$

$\displaystyle =sin(a) + \frac 43sin^3(a)+C$

anti-substitute

$\displaystyle =x +\frac 43x^3+C$

Regardless of what method you use, you should arrive at the same conclusion. Are you sure you copied the problem correctly?