$\int e^{cx}~dx = \dfrac{1}{c}~e^{cx} +C \\$ $\int a^{cx}~dx = \dfrac{1}{c\cdot \ln a}~a^{cx} +C, (\text{for } a>0, a\ne1 )\\$ $\int x \cdot e^{cx}~dx = \dfrac{e^{cx}}{c^2}~(cx-1) +C \\$ $\int x^2 \cdot e^{cx} ~dx= e^{cx}\left(\dfrac{x^2}{c}-\dfrac{2x}{c^2} + \dfrac{2}{c^3}\right) +C\\$ $\int x^n \cdot e^{cx}~dx = \dfrac{1}{c}~x^ne^{cx}-\dfrac{n}{c}\int x^{n-1}e^{cx} dx\\$ $\int \dfrac{e^{cx}}{x} ~dx = \ln|x| + \sum\limits_{i=1}^\infty \dfrac{(cx)^i}{i \cdot i!} +C\\$ $\int \dfrac{e^{cx}}{x^n}~ dx = \dfrac{1}{n-1}\left(-\dfrac{e^{cx}}{x^{n-1}} + c\cdot \int \dfrac{e^{cx}}{x^{n-1}} dx \right)\\$ $\int e^{cx}\cdot \ln x ~dx = \dfrac{1}{c}~ e^{cx}\ln|x| + E_{\,i}(cx) +C\\$ $\int e^{cx}\cdot \sin(bx) ~dx = \dfrac{e^{cx}}{c^2 + b^2}~ \left(c\cdot \sin(bx) - b\cdot cos(bx)\right) +C \\$ $\int e^{cx}\cdot \cos(bx)~ dx = \dfrac{e^{cx}}{c^2 + b^2}~ \left(c\cdot \sin(bx) + b\cdot \cos(bx)\right) +C \\$ $\int e^{cx}\cdot \sin^nx ~dx = \dfrac{e^{cx}\cdot \sin^{n-1}x}{c^2 + n^2}                  ~(c\cdot \sin x - n\cdot \cos(bx)) + \dfrac{n(n-1)}{c^2 + n^2} \int e^{cx} \sin^{n-2} dx\\$ $\int e^{cx}\cdot \cos^nx~ dx = \dfrac{e^{cx}\cdot \cos^{n-1}x}{c^2 + n^2}                  ~(c\cdot \sin x + n\cdot \cos(bx)) + \dfrac{n(n-1)}{c^2 + n^2} \int e^{cx} \cos^{n-2} dx$

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