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Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^...

Evaluate: `inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C`

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To begin with, let’s say
`I = ∫ e^x [f(x) + f ’(x)] dx`
`I = ∫ e^x f(x) dx + ∫ e^x f ’(x) dx `
`= I_1 + ∫ e^x f ’(x) dx … (1)`
Where, `I_1 = ∫ e^x f(x) dx`
Or, `I1 = e^x f(x) – ∫ e^x f ’(x) dx + C` ...
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Evaluate: int e^(x)(f(x)+f'(x))dx=e^(x)f(x)+C

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RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
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  2. intsqrt(x/(1-x))\ dx is equal to sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x...

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  3. Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

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  4. The value of int(sinx+cosx)/(sqrt(1-sin2x))\ dx is equal to sqrt(sin2x...

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  5. If intxsinx\ dx=-xcosx+alpha, then alpha is equal to sinx+C (b) cosx+C...

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  6. int(cos2x-1)/(cos2x+1)\ dx= tanx-x+C (b) x+tanx+C (c) x-tanx+C (d) ...

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  9. int(x^3)/(sqrt(1+x^2))\ dx=a(1+x^2)^(3setminus2)+bsqrt(1+x^2)+C , then...

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  10. int(x^3)/(x+1)\ dx is equal to x+(x^2)/2+(x^3)/3-log|1-x|+C (b) x+(x^...

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  18. Evaluate: int(sinx)/(1+sinx)\ dx

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  19. Evaluate: int(x^2+1)/(x^4+x^2-1) dx

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