Question Type 1: Integrating a polynomial without boundary conditions Exercises

Evaluate the indefinite integral $\int (10x^2 - 5x + 3)\,dx$.

Find $\int (x^3 + 2x^2 + x + 1)\,dx$.

If $\frac{dy}{dx} = 2x^4 - 3x^2 + 1$ and $y(1)=3$, determine $y(x)$.

Find the particular solution of $\frac{dy}{dx} = 8x^4 + 2x^3 + 11x + 3$ given that $y(1)=9$.

Determine the function $y$ if $\frac{dy}{dx} = 4x^3 - x^2 + 6$ and $y(0)=5$.

Find the indefinite integral $\displaystyle\int (x^7 - 3x^5 + 2x^2)\,dx$.

Evaluate the indefinite integral of $3x^4 - x^2 + 7$.

Compute $\displaystyle\int (6x^5 - 4x + 2) \, dx$.

Given that $\frac{dy}{dx} = 7x^3 - 2x + 5$ and $y(2) = 0$, find an expression for $y$ in terms of $x$.

Find the particular solution of $\frac{dy}{dx} = 5x^5 + 4x^3 - 6x$ with the condition $y(0)=10$.

Find the particular solution of $\frac{dy}{dx} = 3x^2 + 8$ satisfying the condition $y(1)=4$.

Find the indefinite integral of $5x^3 + 8x^2 + 9x + 3$.