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Questions  >>  CBSE XII  >>  Math  >>  Integrals
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Q)

Find the integral $\int(2x^2+e^x)\;dx$

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Solution: $\frac{2}{3}x^3 + e^x + k$

Toolbox:

$\int e^{nx} = \frac{1}{n} e^{nx}$

$\int $$x^n$ $=$ $\frac{1}{n+1}$ $x^{n+1}$

Step 1:

$\int 2x^2 = 2.\frac{1}{(2+1)} x^{(2+1)} = \frac{2}{3} x^3$

Step 2:

$\int e^x dx = \frac{1}{1} e^{1.x} = e^x$

Step 3:

Solution = $ \frac{2}{3} x^3 + e^x + k$

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