Find the integral of 2 t 5 + t + 3 with respect to t.

Question

Find the integral of   2      t          5        +  t  +  3 with respect to t.

hi3c4a2nvrgzb · Accepted Answer

Split the single integral into multiple integrals.

$\int 2 t^{5} d t + \int t d t + \int 3 d t$

Since $2$ is constant with respect to $t$ , move $2$ out of the integral.

$2 \int t^{5} d t + \int t d t + \int 3 d t$

By the Power Rule, the integral of $t^{5}$ with respect to $t$ is $\frac{1}{6} t^{6}$ .

$2 (\frac{1}{6} t^{6} + C) + \int t d t + \int 3 d t$

By the Power Rule, the integral of $t$ with respect to $t$ is $\frac{1}{2} t^{2}$ .

$2 (\frac{1}{6} t^{6} + C) + \frac{1}{2} t^{2} + C + \int 3 d t$

Combine $\frac{1}{6}$ and $t^{6}$ .

$2 (\frac{t^{6}}{6} + C) + \frac{1}{2} t^{2} + C + \int 3 d t$

Apply the constant rule.

$2 (\frac{t^{6}}{6} + C) + \frac{1}{2} t^{2} + C + 3 t + C$

Simplify.

$\frac{1}{3} t^{6} + \frac{1}{2} t^{2} + 3 t + C$

Find the integral of 2