# How do you find the integral of #int t/(t^4+16)#?

The answer is

We perform this integral by substitution

Therefore,

So,

Therefore,

By signing up, you agree to our Terms of Service and Privacy Policy

To find the integral of ( \int \frac{t}{t^4 + 16} , dt), you can use the substitution method. Let ( u = t^2 ), then ( du = 2t , dt ). Rewrite the integral with respect to ( u ) as follows: [ \frac{1}{2} \int \frac{1}{u^2 + 16} , du ] This integral can be evaluated using the inverse tangent function. The integral becomes: [ \frac{1}{2} \cdot \frac{1}{4} \arctan \left( \frac{u}{4} \right) + C ] Replace ( u ) with ( t^2 ) and simplify to get the final answer.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7