Question

Evaluate the integral by making the given substitution. (Use C for the constant of integration.)

Answer 1

\[\int\limits_{}^{}\frac{ \sec^2(\frac{ 1 }{ x^9 }) }{ x^{10} }dx\]\[ u = \frac{ 1 }{ x^9 }\]

Answer 2

hint:

u = 1/(x^9) = x^(-9)

du/dx = -9x^(-10)

du = -9x^(-10)*dx

-du/9 = x^(-10)dx

(1/x^10)dx = -du/9

Answer 3

\[du= 1 / x^9 = \frac{ x^{-10} }{ -10 }\]
\[-10du = \frac{ 1 }{ x^{10} }\]
\[\int\limits_{}^{}\sec^2(\frac{ 1 }{ x^9 })(\frac{ 1 }{ x^{10} })dx = \int\limits_{}^{}\sec^2u(-10du)\]
\[-10\int\limits_{}^{}\sec^2udu = -10tanu +C = -10\tan(1/x^9)+C\]

Well, that is my attempt

Answer 4

let me know if the hint helps or not

Answer 5

your answer is close but not quite there

Answer 6

Yea, got it now with that hint, I didn't do the anti-derivative of x^-9 correctly. The answer is: \[-\frac{ 1 }{ 9 }\tan(\frac{ 1 }{ x^9 })+C\]

Answer 7

Thanks :)

Answer 8

yep you nailed it