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Popular >

integral of 2^x+2x

Solution

\int 2^{x} + 2 x d x

Solution

\frac{2 ^{x}}{ln ( 2 )} + x^{2} + C

Solution steps

\int 2^{x} + 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2^{x} d x + \int 2 x d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 2 x d x = x^{2}

= \frac{2 ^{x}}{ln ( 2 )} + x^{2}

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + x^{2} + C

Popular Examples

integral of e^{1/(3x)}

\int e^{\frac{1}{3 x}} d x

integral of x^{-17/10}

\int x^{- \frac{17}{10}} d x

integral of (x^2-2x)cos(x)

\int (x^{2} - 2 x) cos (x) d x

integral of t/((t^2+1)^2)

\int \frac{t}{( t ^{2} + 1 ) ^{2}} d t

integral of 1/(sin(5x))

\int \frac{1}{sin ( 5 x )} d x

Frequently Asked Questions (FAQ)

What is the integral of 2^x+2x ?
The integral of 2^x+2x is (2^x)/(ln(2))+x^2+C