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Solution Steps
Integrate the sum term by term.
Factor out the constant in each of the terms.
Since for , replace with . Multiply times .
Find the integral of using the table of common integrals rule .
If is an antiderivative of , then the set of all antiderivatives of is given by . Therefore, add the constant of integration to the result.
Differentiate w.r.t. x
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\int 7x\mathrm{d}x+\int 8\mathrm{d}x
Integrate the sum term by term.
7\int x\mathrm{d}x+\int 8\mathrm{d}x
Factor out the constant in each of the terms.
\frac{7x^{2}}{2}+\int 8\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{\left(k+1\right)}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 7 times \frac{x^{2}}{2}.
\frac{7x^{2}}{2}+8x
Find the integral of 8 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{7x^{2}}{2}+8x+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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