Primitive function

9000071209

Level:

Evaluate the following integral on \(\mathbb{R}\). \[ \int \cos ^{3}x\sin x\, \mathrm{d}x \]

\(-\frac{\cos ^{4}x} {4} + c,\ c\in \mathbb{R}\)

\(-\frac{\sin ^{4}x\cos x} {4} + c,\ c\in \mathbb{R}\)

\(- 3\cos ^{2}x + c,\ c\in \mathbb{R}\)

Level:

Evaluate the following integral on \(\mathbb{R}\). \[ \int (x + 2)\cos x\, \mathrm{d}x \]

\((x + 2)\sin x +\cos x + c,\ c\in \mathbb{R}\)

\(-\left (\frac{x^{2}} {2} + 2x\right )\sin x + c,\ c\in \mathbb{R}\)

\((x + 2)\sin x -\sin x + c,\ c\in \mathbb{R}\)

Level:

Evaluate the following integral on \(\mathbb{R}\). \[ \int \cos x\cdot \left (-3 +\sin x\right )^{5}\, \mathrm{d}x \]

\(\frac{\left (-3+\sin x\right )^{6}} {6} + c\text{, }c\in \mathbb{R}\)

\(6\left (-3 +\sin x\right )^{6} + c,\ c\in \mathbb{R}\)

\(\frac{\left (-3+\cos x\right )^{6}} {6} + c,\ c\in \mathbb{R}\)

\(6\left (-3 +\cos x\right )^{6} + c,\ c\in \mathbb{R}\)