 # What is &#x222B;<!-- ∫ --> ( t <mrow class="MJX-TeXAtom-ORD"> 4 </mrow> Jaylene Duarte 2022-04-04 Answered
What is $\int \left({t}^{4}-2{t}^{3}-1\right)﻿dt$?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Taniya Wood

Remove parentheses.

$\int {t}^{4}-2{t}^{3}-1dt$

Split the single integral into multiple integrals.

$\int {t}^{4}dt+\int -2{t}^{3}dt+\int -1dt$

By the Power Rule, the integral of ${t}^{4}$ with respect to $t$ is $\frac{1}{5}{t}^{5}$.

$\frac{1}{5}{t}^{5}+C+\int -2{t}^{3}dt+\int -1dt$

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

$\frac{1}{5}{t}^{5}+C-2\int {t}^{3}dt+\int -1dt$

By the Power Rule, the integral of ${t}^{3}$ with respect to $t$ is $\frac{1}{4}{t}^{4}$.

$\frac{1}{5}{t}^{5}+C-2\left(\frac{1}{4}{t}^{4}+C\right)+\int -1dt$

Apply the constant rule.

$\frac{1}{5}{t}^{5}+C-2\left(\frac{1}{4}{t}^{4}+C\right)-t+C$

Simplify.

$\frac{{t}^{5}}{5}-\frac{{t}^{4}}{2}-t+C$

Reorder terms.

$\frac{1}{5}{t}^{5}-\frac{1}{2}{t}^{4}-t+C$