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Integrals (27 questions)

QuestionAnswer
$\int \frac{7}{4x} dx$ $\frac{7}{4} \ln \vert x \vert + C$
$ \int x^2 dx $ $ \frac{1}{3} x^3 + c $
$\int (x+2)dx$ $\frac{x^2}{2} + 2x + C$
$\int x^{-1/3}dx$ $\frac{3 x^{2/3}}{2} + C$
$\int -3 \cos(x) dx$ $-3 \sin(x) + C$
$\int \frac{1}{2\sqrt{x}}dx$ $\sqrt{x} + C$
$\int x^3 - 6 x^2 + 7 dx$ $\frac{x^4}{4} - 2 x^3 + 7x + C$
$\int 5 - x^2 + 6 x^4 dx$ $5x - \frac{x^3}{3} + \frac{6 x^5}{5} + C$
$\int \sqrt[4]{x^3} dx$ $\frac{4x^{7/4}}{7} + C$
$\int 4 e^xdx$ $4 e^x + C$
$\int 4 e^x dx$ $4 e^x + C$
$\int 7 x^{-2}dx$ $-7 x^{-1} + C$
$\int \sqrt[4]{x} dx$ $\frac{4 x^{5/4}}{5} + C$
$\int x(1+3x^5) dx$ $\frac{1}{2} x^2 + \frac{3}{7} x^7 + C$
$\int (4x + 1)^2 dx$ $\frac{16}{3} x^3 + 4x^2 + x + C$
$\int \sqrt{2x} dx$ $\frac{2 \sqrt{2}}{3} x^{3/2}+C$
$\int \frac{3x^3 - 2x }{x}dx$ $x^3 - 2x + C$
$\int 2x - e^x dx$ $x^2 - e^x + C$
$\int (x^2 +5 x - 1) dx$ $\frac{x^3}{3} + \frac{5x^2}{2} - x + C$
$\int \frac{1 + \cos^2(x)}{\cos^2(x)}dx$ $\tan(x) + x + C$
$\int x(\sqrt{x} + 1) dx$ $\frac{2x^{5/2}}{5} + \frac{x^2}{2} + C$
$\int (2-x)(1+3x) dx$ $-x^3 + \frac{5x^2}{2} + 2x + C$
$\int \frac{4}{1+x^2} dx$ $4 \arctan(x) + C$
$\int \sqrt{\frac{5}{x}} dx$ $2 \sqrt{5x} + C$
$\int \frac{4}{x^3} dx$ $\frac{-2}{x^2} + C$
$\int \frac{5}{3x} dx$ $\frac{5}{3} \ln \vert x\vert + C$

\begin{displaymath}\int \frac{7}{4} dx\end{displaymath}


\begin{displaymath}\frac{7x}{4} + C\end{displaymath}