\(\displaystyle \int_{-1}^{1}\log\!\left(\frac{3+x}{\,3-x\,}\right)dx=\ \ ?\)
The adjoint (adjugate) of the matrix \(\begin{bmatrix}1&2 \\ 3&4\end{bmatrix}\) is
If \(A=\begin{bmatrix}1&0 \\ 0&1\end{bmatrix}\), then the value of \(A^{25}\) is
If a binary operation is defined by \(a\ \mathrm{o}\ b=3a+b\), then \((2\ \mathrm{o}\ 3)\ \mathrm{o}\ 5=\) ?
\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?
\(\sin^{-1}x+\sin^{-1}y=\) (principal values)
For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).
For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).
If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?
\(\dfrac{d}{dx}\big(e^{x}+\cos5x\big)=\) ?
\(\dfrac{d}{dx}\!\left(\dfrac{1}{4}\sec4x\right)=\) ?
\(\dfrac{d}{dx}\big(\log_{e}(10x)\big)=\) ?
\(\displaystyle \int \sin\!\left(\frac{3x}{4}\right)\,dx=\) ?
\(\displaystyle \int \cos\!\left(\frac{7x}{9}\right)\,dx=\) ?
\(\displaystyle \int \sec^{2}\!\left(\frac{17x}{23}\right)\,dx=\) ?