Question

Evaluate the ∫(t³+3t/t²+1)dt

Answer 1

Solution:

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$\int t^3dt=\dfrac{t^4}{4}$

$\int \dfrac{3t}{t^2}dt=3ln|t|$

$\int 1dt=t$

$\int \:t^3dt+\int \frac{3t}{t^2}dt+\int \:1dt=\dfrac{t^4}{4}+3ln|t|+t+C$

Answer:

$\dfrac{t^4}{4}+3ln|t|+t+C$