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Integrals / Substitution (15 questions)

QuestionAnswer
$\int \cos(4x) dx$ $\frac{1}{4} \sin(4x) + C$
$\int x(3+x^2)^9 dx$ $\frac{1}{20} (3+x^2)^{10} +C$
$\int (5x-3)^7dx$ $\frac{1}{40} (5x-3)^8 +C$
$\int \frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ $-2 \cos(\sqrt{x}) + C$
$\int \frac{\sin(\ln(x))}{x}dx$ $-\cos(\ln(x)) + C$
$\int \sin(2x) dx$ $\frac{-\cos(2x)}{2}$
$\int \sin(2x) dx$ $\frac{-\cos(2x)}{2}+C$
$\int 2x(x^2+8)^9 dx$ $\frac{(x^2+8)^{10}}{10} +C$
$\int x^2 \sqrt{x^3+5}dx$ $\frac{2(x^3+5)^{3/2}}{9}+C$
$\int \frac{6x^2+5}{(2x^3+5x)^4}dx$ $\frac{-1}{3(2x^3+5x)^3}+C$
$\int \frac{6x+7}{(3x^2 + 7x + 4)^2}dx$ $\frac{-1}{3x^2+7x+4}+C$
$\int \frac{dx}{3-5x}$ $\frac{-1}{5} \ln\vert 3-5x\vert + C$
$\int \frac{x}{\sqrt{1-3x^2}} dx$ $\frac{-1}{3} \sqrt{1-3x^2} + C$
$\int \frac{2 x}{(1+4x^2)^3} dx$ $\frac{-1}{8(1+4x^2)^2} + C$
$\displaystyle{\int \frac{2 x}{(1+4x^2)^3} dx}$

\begin{displaymath}\frac{-1}{8(1+4x^2)^2} + C\end{displaymath}