What is the integral of ra^r ?

The integral of ra^r is (a^rr)/(ln(a))-(a^r)/(ln^2(a))+C

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integral of ra^r

\int r a^{r} d r

\frac{a ^{r} r}{ln ( a )} - \frac{a ^{r}}{ln ^{2} ( a )} + C

Solution steps

\int r a^{r} d r

Apply Integration By Parts

: \frac{a ^{r} r}{ln ( a )} - \int \frac{a ^{r}}{ln ( a )} d r

= \frac{a ^{r} r}{ln ( a )} - \int \frac{a ^{r}}{ln ( a )} d r

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

= \frac{a ^{r} r}{ln ( a )} - \frac{a ^{r}}{ln ^{2} ( a )}

Add a constant to the solution

= \frac{a ^{r} r}{ln ( a )} - \frac{a ^{r}}{ln ^{2} ( a )} + C

\int (x + 1)^{5} d x

\frac{d}{d x} ([x + (x + sin^{2} (x))^{5}]^{3})

\int - \frac{2000 t}{( 1 + t ^{2} )} d t

\frac{d}{d x} (4 x^{2} + x)

x^{2} - 6 x

What is the integral of ra^r ?
The integral of ra^r is (a^rr)/(ln(a))-(a^r)/(ln^2(a))+C