Home
Class 12
MATHS
int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1)...

`int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1))dx`.

Text Solution

Verified by Experts

Let `x+tan^(-1)x=t`
` :. (1+(1)/(x^(2)+1))dx=dt " or "((x^(2)+2)/(x^(2)+1))dx=dt`
` :. int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1))dx=int 5^(t) dt`
`=(5^(t))/(log_(e)5)+c`
`=(5^(x+tan^(-1)x))/(log_(e)5)+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int (e^(tan^(-1)x)dx)/((1+x^(2))^(2))

int (e^(2 tan^(-1)x)(1+x)^(2)dx)/(1+x^(2))

Integrate : int (e^(m tan^(-1)x))/((1+x^(2))^((3)/(2)))dx

int (sin (tan^(-1)x)dx)/(1+x^(2))

int (tan^(-1)x dx)/((1+x^(2))^((3)/(2))

int_(0)^(1)x(tan^(-1)x)^(2)dx

int(x^(2) sin^(-1)x)/((1-x^(2))^((5)/(2)))dx

int e^(x).(x^(2)+1)/((x+1)^(2))dx

int(e^(x)(1+x^(2)))/((1+x)^(2))dx

int ((x^(2)-1)dx)/(x^(4) + x^(2) + 1)