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Popular >

integral of (qe^q+q)

Solution

\int (q e^{q} + q) d q

Solution

e^{q} q - e^{q} + \frac{q ^{2}}{2} + C

Solution steps

\int q e^{q} + q d q

Apply the Sum Rule:

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

= \int q e^{q} d q + \int q d q

\int q e^{q} d q = e^{q} q - e^{q}

\int q d q = \frac{q ^{2}}{2}

= e^{q} q - e^{q} + \frac{q ^{2}}{2}

Add a constant to the solution

= e^{q} q - e^{q} + \frac{q ^{2}}{2} + C

Popular Examples

integral of (5x)/(3x^2+1)

\int \frac{5 x}{3 x ^{2} + 1} d x

integral of (3x+108)/(x^2+2x-48)

\int \frac{3 x + 108}{x ^{2} + 2 x - 48} d x

integral of y^2 integral

y^{2}

integral of (sin^2(x/2))/(1-cos^2(x))

\int \frac{sin ^{2} ( \frac{x}{2} )}{1 - cos ^{2} ( x )} d x

integral of ((2+x+x^2))/(sqrt(x))

\int \frac{( 2 + x + x ^{2} )}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (qe^q+q) ?
The integral of (qe^q+q) is e^qq-e^q+(q^2)/2+C