#### To determine

**To find:**

∫tt2+3t+2dt

#### Answer

27t72+65t52+43t32+C

#### Explanation

**1) Concept:**

Apply the formula of indefinite integral and simplify.

**2) Formula:**

∫xndx=xn+1n+1+C

**3) Calculation:**

Consider,

∫tt2+3t+2dt

The integral can be rewritten as

∫tt2+3t+2dt

=∫t52+3t32+2t12dt

=∫t52 dt+∫3t32 dt+∫2t12 dt

Taking the constants outside the integral,

=∫t52 dt+3∫t32 dt+2∫t12 dt

By applying the formula of integral, we get

=t7272+3t5252+2t3232+C

Thus by simplifying,

∫tt2+3t+2dt=27t72+65t52+43t32+C

**Conclusion:**

∫tt2+3t+2dt=27t72+65t52+43t32+C