Integral Problem

Use formal substitution to find the integral of:
(1 + 1/t)^3 * (1 / t^2)dt

Any help is much appreciated!

Quote:

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Originally Posted by cupcakelova87

Use formal substitution to find the integral of:
(1 + 1/t)^3 * (1 / t^2)dt

Any help is much appreciated!

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int[(1 + (1/t))^3 + (1/(t^2))dt]

Expand:

int[(t^3 + 3t^2 + 4t + 1)/t^3]

Expand further:

int[(3/t) + (4/t^2) + (1/t^3) + 1]

Thus,

int[(3/t) + (4/t^2) + (1/t^3) + 1] = 3*ln(t) + (-4/t) + (-1/(2*t^2)) + t + C

= 3*ln(t) - 4/t - 1/(2t^2) + t + C

Quote:

---

Originally Posted by cupcakelova87

Use formal substitution to find the integral of:
(1 + 1/t)^3 * (1 / t^2)dt

Any help is much appreciated!

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Let x = 1 + 1/t. Then dx = -1/t^2 dt

So:
Int[(1 + 1/t^2)^3 * (1/t^2) dt]

= Int[-(1 + 1/t^2)^3 * (-1/t^2) dt]

= Int[-x^3 * dx]

= -(1/4)x^4 + C

= -(1/4)*(1 + 1/t)^4 + C

-Dan