evaluate √3x^2+4x−7 dx
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Answer:
We have,
∫
3x
2
−4x+5
dx
⇒∫
3(x
2
−
3
4
x+
3
5
)
dx
⇒∫
3
(x
2
−
3
4
x+
3
5
)
dx
On adding and subtracting coefficient of x
Then,
(
6
4
)
2
=
9
4
Then,
∫
3
x
2
−
3
4
x+
9
4
−
9
4
+
3
5
dx
⇒∫
3
(x−
3
2
)
2
−
9
11
dx
⇒∫
3
(x−
3
2
)
2
−(
3
11
)
2
dx
On applying
∫
x
2
−a
2
dx=
2
x
x
2
−a
2
−
2
a
2
ln
∣
∣
∣
x+
x
2
−a
2
∣
∣
∣
∫
3
(x−
3
2
)
2
−(
3
11
)
2
dx=
2
(x−
3
2
)
(x−
3
2
)
2
−(
3
11
)
2
−
2
(
3
11
)
2
ln
∣
∣
∣
∣
∣
∣
∣
(x−
3
2
)+
(x−
3
2
)
2
−(
3
11
)
2
∣
∣
∣
∣
∣
∣
∣
Hence, this is the answer.
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