Integral Calculus

Match the items on the right to the items on the left.

\int \frac{1}{a \sin x + b \cos x} d x

\int e^{k x} \{k f (x) + f' (x)\} d x

\int e^{a x} \sin b x d x

\int e^{a x} \cos b x d x

\int \sqrt{a^{2} - x^{2}} d x

\frac{1}{\sqrt{a^{2} + b^{2}}} \log |\tan (\frac{x}{2} + \frac{1}{2} \tan^{- 1} \frac{b}{a})| + C

e^{k x} f (x) + C

\frac{e^{a x}}{a^{2} + b^{2}} (a \sin b x - b \cos b x) + C

\frac{e^{a x}}{a^{2} + b^{2}} (a \cos b x + b \sin b x) + C

\frac{1}{2} x \sqrt{a^{2} - x^{2}} + \frac{1}{2} a^{2} \sin^{- 1} (\frac{x}{a}) + C